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PD Dr. Martin Väth - List of Publications

Monographs and Text Books

  1. Väth, M., Ideal spaces, Lect. Notes Math., no. 1664, Springer, Berlin, Heidelberg, 1997. Download corrigenda (PDF) Download corrigenda (LaTeX).
  2.            , Volterra and integral equations of vector functions, Marcel Dekker, New York, Basel, 2000.
  3.            , Integration theory. A second course, World Scientific Publ., Singapore, New Jersey, London, Hong Kong, 2002. Download corrigenda (PDF) Download corrigenda (LaTeX).
  4. Appell, J. and Väth, M., Elemente der Funktionalanalysis, Vieweg & Sohn, Braunschweig, Wiesbaden, 2005.
  5. Väth, M., Nonstandard analysis, Birkhäuser, Basel, 2007. Download corrigenda (PDF).
  6.            , Topological analysis. From the basics to the triple degree for nonlinear Fredholm inclusions, de Gruyter, Berlin, New York, 2012.

Invited Contributions

  1. Dirr, G. and Väth, M., Continuity of near-duality maps and characterizations of ideal spaces of measurable functions, Recent Trends in Nonlinear Analysis (Appell, J., ed.), Festschrift Dedicated to Alfonso Vignoli on the Occasion of his Sixtieth Birthday, Birkhäuser, 2000, 139-148.
  2. Väth, M., Riesz spaces and ideals of measurable functions, Handbook of Measure Theory (Pap, E., ed.), North-Holland, Amsterdam, Boston, London, 2002, 787-825.

Research Papers

  1. Appell, J. and Väth, M., Weakly singular Hammerstein-Volterra operators in Orlicz and Hölder spaces, Z. Anal. Anwendungen 12 (1993), no. 4, 663-676.
  2. Väth, M., A general theorem on continuity and compactness of the Uryson operator, J. Integr. Equ. Appl. 8 (1996), 379-389.
  3. Chen, C.-J. and Väth, M., On the L-characteristic of the superposition operator in Lebesgue spaces with mixed norm, Z. Anal. Anwendungen 16 (1997), no. 2, 377-386.
  4. Väth, M., Approximation, complete continuity, and uniform measurability of the Uryson operator on general measure spaces, Nonlinear Anal. 33 (1998), no. 7, 715-728.
  5.            , Abstract Volterra equations of the second kind, J. Integr. Equ. Appl. 10 (1998), no. 3, 319-362.
  6.            , Complete continuity of some nonlinear Volterra operator in Banach spaces, Z. Anal. Anwendungen 17 (1998), no. 1, 23-35.
  7.            , The dual space of L is L1, Indag. Math. 9 (1998), no. 4, 619-625.
  8. Appell, J., Väth, M., and Zabrejko, P. P., On the averaging method for linear differential equations in Banach spaces, Progr. Math. (Allahabad) 32 (1998), no. 2, 1-14.
  9. Väth, M. and Zabrejko, P. P., A theorem about differentiability of solutions of ordinary differential equations with respect to a parameter, Analysis 19 (1999), 397-400.
  10. Appell, J. and Väth, M., The space of Carathéodory functions, Trudy Inst. Mat. NAN Belarus. Minsk. 2 (1999), 39-43.
  11. Appell, J., Väth, M., and Vignoli, A., Compactness and existence results for ordinary differential equations in Banach spaces, Z. Anal. Anwendungen 18 (1999), no. 3, 569-584.
  12. Väth, M., A compactness criterion of mixed Krasnoselskij-Riesz type in regular ideal spaces of vector functions, Z. Anal. Anwendungen 18 (1999), no. 3, 713-732.
  13. Biberdorf, E. A. and Väth, M., On the spectrum of orthomorphisms and Barbashin operators, Z. Anal. Anwendungen 18 (1999), no. 4, 859-873.
  14. Väth, M., Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal. 13 (1999), no. 2, 341-363.
  15. Santucci, P. and Väth, M., On the definition of eigenvalues for nonlinear operators, Nonlinear Anal. 40 (2000), 565-576, (special issue dedicated to V. Lakshmikantham).
  16. Väth, M., An axiomatic approach to a coincidence index for noncompact function pairs, Topol. Methods Nonlinear Anal. 16 (2000), no. 2, 307-338.
  17. Luxemburg, W. A. J. and Väth, M., The existence of non-trivial bounded functionals implies the Hahn-Banach extension theorem, Z. Anal. Anwendungen 20 (2001), no. 2, 267-279.
  18. Väth, M., On the connection of degree theory and 0-epi maps, J. Math. Anal. Appl. 257 (2001), 223-237.
  19. Appell, J., Giorgieri, E., and Väth, M., On a class of maps related to the Furi-Martelli-Vignoli spectrum, Ann. Mat. Pura Appl. 179 (2001), 215-228.
  20. Väth, M., Fixed point free maps of a closed ball with small measures of noncompactness, Collect. Math. 52 (2001), no. 2, 101-116.
  21. Giorgieri, E. and Väth, M., A characterization of 0-epi maps with a degree, J. Funct. Anal. 187 (2001), 183-199.
  22. Appell, J., Väth, M., and Vignoli, A., F-epi maps, Topol. Methods Nonlinear Anal. 18 (2001), 373-393.
  23. Appell, J., D'Aniello, E., and Väth, M., Some remarks on small sets, Ricerche Mat. L (2001), no. 2, 255-274.
  24. Appell, J. and Väth, M., Misure di non compattezza di insiemi ed operatori integrali in spazi di funzioni misurabili, Rend. Mat. Appl. (7) 21 (2001), 159-190.
  25. Santucci, P. and Väth, M., Grasping the phantom - A new approach to nonlinear spectral theory, Ann. Mat. Pura Appl. 180 (2001), no. 3, 255-284.
  26. Väth, M., Coincidence points of function pairs based on compactness properties, Glasgow Math. J. 44 (2002), no. 2, 209-230.
  27. Ricker, W. J. and Väth, M., An extension of a commutativity theorem of M. Uchiyama, Irish Math. Soc. Bull. 48 (2002), 35-41.
  28. Appell, J., D'Aniello, E., and Väth, M., Errata and addendum to ``Some remarks on small sets'', Ricerche Mat. 54 (2005), no. 1, 211-213.
  29. Ricker, W. J. and Väth, M., The Weyl calculus and commutativity of selfadjoint matrices and operators, Tübinger Berichte zur Funktionalanalysis 11 (2001/2002), 279-294.
  30. Väth, M., On the minimal displacement problem of γ-Lipschitz maps and γ-Lipschitz retractions onto the sphere, Z. Anal. Anwendungen 21 (2002), no. 4, 901-914.
  31. Appell, J., Giorgieri, E., and Väth, M., Nonlinear spectral theory for homogeneous operators, Nonlinear Funct. Anal. Appl. 7 (2002), no. 4, 589-618.
  32. Andres, J. and Väth, M., Coincidence index for noncompact mappings on nonconvex sets, Nonlinear Funct. Anal. Appl. 7 (2002), no. 4, 619-658.
  33. Väth, M., Coepi maps and generalizations of the Hopf extension theorem, Topology Appl. 131 (2003), 79-99.
  34. Ricker, W. J. and Väth, M., Spaces of complex functions and vector measures in incomplete spaces, J. Function Spaces Appl. 2 (2004), 1-16.
  35. Andres, J. and Väth, M., Two topological definitions of a Nielsen number for coincidences of noncompact maps, Fixed Point Theory Appl. 2004 (2004), no. 1, 49-69.
  36. Appell, J., Erzakova, N. A., Santana, S. F., and Väth, M., On some Banach space constants arising in nonlinear fixed point and eigenvalue theory, Fixed Point Theory Appl. 2004 (2004), no. 4, 317-336.
  37. Salem, H. A. H. and Väth, M., An abstract Gronwall lemma and applications to global existence results for functional differential and integral equations of fractional order, J. Integr. Equ. Appl. 16 (2004), no. 4, 411-439.
  38. Väth, M., Convergence theorems and measures of noncompactness for noncompact Urysohn operators in ideal spaces, J. Integr. Equ. Appl. 16 (2004), no. 1, 67-82.
  39.            , Global bifurcation of the p-Laplacian and related operators, J. Differential Equations 213 (2005), no. 2, 389-409.
  40. Eisner, J., Kučera, M., and Väth, M., Degree and global bifurcation of elliptic equations with multivalued unilateral conditions, Nonlinear Anal. 64 (2006), 1710-1736.
  41. Väth, M., Compactness estimates for integral operators of vector functions with nonmeasurable kernels, J. Integr. Equ. Appl. 18 (2006), no. 1, 59-81.
  42. Kim, I.-S. and Väth, M., Some results on the extension of single- and multivalued maps, Topol. Methods Nonlinear Anal. 28 (2006), 133-153.
  43. Väth, M., Some measurability results and applications to spaces with mixed family-norm, Positivity 10 (2006), no. 4, 737-753.
  44.            , Global nontrivial bifurcation of homogeneous operators with an application to the p-Laplacian, J. Math. Anal. Appl. 321 (2006), no. 1, 343-352.
  45.            , Merging of degree and index theory, Fixed Point Theory Appl. 2006 (2006), Article ID 36361, 30 pages.
  46.            , Continuity of single- and multivalued superposition operators in generalized ideal spaces of measurable vector functions, Nonlinear Functional Anal. Appl. 11 (2006), no. 4, 607-646.
  47.            , Global solution branches and a topological implicit function theorem, Ann. Mat. Pura Appl. 186 (2007), no. 2, 199-227.
  48. Andres, J. and Väth, M., Calculation of Lefschetz and Nielsen numbers in hyperspaces for fractals and dynamical systems, Proc. Amer. Math. Soc. 135 (2007), 479-487.
  49. Appell, J., Chen, C.-J., Tseng, S., and Väth, M., A continuation and existence result for a boundary value problem on an unbounded domain arising for the electrical potential in a cylindrical double layer, J. Math. Anal. Appl. 332 (2007), 1134-1147.
  50. Väth, M., Degree and index theories for noncompact function triples, Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 79-118.
  51. Kim, I.-S. and Väth, M., Some remarks on measures of noncompactness and retractions onto spheres, Topology Appl. 154 (2007), 3056-3069.
  52. Väth, M., Continuity, compactness, and degree theory for operators in systems involving p-Laplacians and inclusions, J. Differential Equations 245 (2008), 1137-1166.
  53. Appell, J., Chen, C.-J., Tseng, S., and Väth, M., Iterative approximation for a boundary value problem arising for the electrical potential on a cylindrical double layer, J. Anal. Appl. 27 (2008), no. 3, 283-300.
  54. Väth, M., A disc-cutting theorem and two-dimensional bifurcation, CUBO 10 (2008), no. 4, 85-100.
  55. Eisner, J., Kučera, M., and Väth, M., Global bifurcation of a reaction-diffusion system with inclusions, J. Anal. Appl. 28 (2009), no. 4, 373-409.
  56. Väth, M., New beams of global bifurcation points for a reaction-diffusion system with inequalities or inclusions, J. Differential Equations 247 (2009), 3040-3069.
  57. Eisner, J., Kučera, M., and Väth, M., Bifurcation points for a reaction-diffusion system with two inequalities, J. Math. Anal. Appl. 365 (2010), 176-194.
  58. Kim, Y.-H. and Väth, M., Global solution branches for equations involving nonhomogeneous operators of p-Laplace type, Nonlinear Anal. 74 (2011), no. 5, 1878-1891.
  59. Väth, M., Bifurcation for a reaction-diffusion system with unilateral obstacles with pointwise and integral conditions, Nonlinear Anal.: Real World Appl. 12 (2011), 817-836.
  60. Appell, J., Guanda, N., and Väth, M., Function spaces with the Matkowski property and degeneracy phenomena for composition operators, Fixed Point Theory 12 (2011), no. 2, 265-284.
  61. Eisner, J. and Väth, M., Location of bifurcation points for a reaction-diffusion system with Neumann-Signorini conditions, Advanced Nonlinear Studies 11 (2011), 809-836.
  62. Väth, M., Compactness of linear integral operators in ideal spaces of vector functions, J. Integr. Equ. Appl. 24 (2012), no. 3, 393-411.
  63.            , Continuity and differentiability of multivalued superposition operators with atoms and parameters I, J. Anal. Appl. 31 (2012), 93-124.
  64. Kučera, M. and Väth, M., Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions, J. Differential Equations 252 (2012), 2951-2982.
  65. Väth, M., Continuity and differentiability of multivalued superposition operators with atoms and parameters II, J. Anal. Appl. 31 (2012), 139-160.
  66. Baltaev, J. I., Kučera, M., and Väth, M., A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions, Applications of Math. 57 (2012), no. 2, 143-165.
  67. Väth, M., A general degree for function triples, Topol. Methods Nonlinear Anal. 41 (2013), no. 1, 163-190.
  68. Benedetti, I., Taddei, V., and Väth, M., Evolution problems with nonlinear nonlocal boundary conditions, J. Dynam. Differential Equations 25 (2013), no. 2, 477-503.
  69. Väth, M., Bifurcation of obstacle problems with inclusions follow from degree results for variational inequalities, Differential Integral Equations 26 (2013), no. 11-12, 1235-1262.
  70.            , Calculation of degree and global bifurcation for variational inequalities with nonsymmetric operators in Banach spaces, Ann. Mat. Pura Appl. 193 (2014), no. 1, 237-259.
  71. Kim, I.-S. and Väth, M., The Krasnosel'skij-Quittner formula and instability of a reaction-diffusion system with unilateral obstacles, Dynamics of Partial Differential Equations 11 (2014), no. 3, 229-250.
  72. Eisner, J., Kučera, M., and Väth, M., A variational approach to bifurcation points of a reaction-diffusion system with obstacles and Neumann boundary conditions, Applications of Math. 61 (2016), no. 1, 1-25.
  73. Eisner, J. and Väth, M., Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas, Nonlinear Anal. 135 (2016), 158-193.
  74. Kim, I.-S. and Väth, M., A degree theory for variational inequalities with sums of maximal monotone and (S+) operators, Topol. Methods Nonlinear Anal. 47 (2016), no. 2, 405-422.
  75. Benedetti, I. and Väth, M., Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces, Topol. Methods Nonlinear Anal. (2016), 613-636.
  76. Gurevich, P. and Väth, M., Stability for semilinear parabolic problems in L2 and W1,2, Z. Anal. Anwendungen (2016), no. 3, 333-357.
  77. Erzakova, N. A. and Väth, M., On strongly condensing operators, Ann. Mat. Pura Appl. 196 (2017), no. 1, 309-323.
  78. Recke, L., Väth, M., Kučera, M., and Navrátil, J., Crandall-Rabinowitz type bifurcation for non-differentiable perturbations of smooth mappings, Patterns of Dynamics. Berlin, July 2016 (Berlin, Heidelberg, New York) (Gurevich, P., Hell, J., Sandstede, B., and Scheel, A., eds.), Springer Proceedings in Mathematics & Statistics, vol. 205, Springer, 2017, (to appear).
  79. Väth, M., Some Crandall-Rabinowitz type results and applications to reaction-diffusion systems, J. Math. Anal. Appl. (2018), (to appear).

Conference Proceedings and Surveys

  1.            , Complete continuity of the Uryson operator, Nonlinear Analysis. Theory, Methods & Applications (Athens, Greece 1996) (Lakshmikantham, V., ed.), vol. 30, Proc. Sec. World Congr. Nonlin. Anal., no. 1, Pergamon, 1997, 527-534.
  2.            , Linear and nonlinear abstract Volterra equations, Funct. Differ. Equ. 5 (1998), no. 3-4, 499-512.
  3.            , The Furi-Martelli-Vignoli spectrum vs. the phantom, Nonlinear Analysis. Theory, Methods & Applications (Catania, Sicily 2000) (Lakshmikantham, V., ed.), Proc. Third World Congr. Nonlin. Anal., vol. 47, Pergamon, 2001, 2237-2248.
  4.            , Schinkenbrote und Nichtlineare Analysis, Eichstätter Koll. Did. Math. 73 (2003), 1-7.
  5.            , Einige topologische Methoden in der nichtlinearen Analysis, Jahresber. Deutsch. Math.-Verein. 106 (2004), no. 3, 129-147.
  6.            , Generalized ideal spaces and applications to the superposition operator, Proceedings of the Conference Positivity IV--Theory and Applications, 2005 (Dresden) (Weber, M. R. and Voigt, J., eds.), Techn. Univ. Dresden, 2006, 147-154.
  7.            , The essential spectral radius of Volterra operators and an application to Volterra-Hammerstein functional inclusions, Positivity 13 (2009), no. 1, 287-298.
  8.            , Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities, Math. Bohem. (Prague, 2013), vol. 139, Proceedings of Equadiff 13, no. 2, 2014, 195-211.