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Quasi-bounded mappings and complementarity problems depending of parameters

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Abstract

In this paper are presented a mathematical tool based on the notion of quasi-bounded mapping, applicable to the study of nonlinear complementarity problems depending of parameters.

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References

  1. Adly, S., Goeleven, D., Théra, M.: Recession mapping and noncoercive variational inequalities. Nonlinear Anal. Theory Meth. Appl. 26(9), 1573–1603 (1996). doi:10.1016/0362-546X(94)00364-N

    Article  Google Scholar 

  2. Akhmerov, R.R., Kamenskii, M.I., Potapov, A.S., Rodkina, A.E., Sadovskii, B.N.: Measures of Noncompactness and Condensing Operators. Birkhäuser Verlag (1992)

  3. Amann, H.: Lecture on Some Fixed Point Theorems, IMPA. Rio de Janeireo-GB (1974)

  4. Ayerbe Toledano, J.M., Dominguez Benavides, T., Lopez Acedo, G.: Measure of Noncompactness in Metric Fixed Point Theory. Birkhäuser Verlag (1997)

  5. Banas, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Marcel Dekker Inc. (1980)

  6. Bezine G., Cimetière A., Gelbert J.P.: Unilateral buckling of thin elastic plates by the boundary integral equation methods. Int. J. Numer. Meth. Eng. 21, 2189–2199 (1985). doi:10.1002/nme.1620211206

    Article  Google Scholar 

  7. Bourbaki N.: Topologie Générale. Hermann, Paris (1960)

    Google Scholar 

  8. Brezis H., Nirenberg L.: Characterization of the ranges of some nonlinear operators and applications to boundary value problems. Ser. IV. Ann. Scuola Normale Superiore Pisa, Classe di Scienze 2, 225–326 (1978)

    Google Scholar 

  9. Cain G.L. Jr, Nashed M.Z.: Fixed points and stability for a sum of two operators in locally convex spaces. Pac. J. Math. 39(3), 581–592 (1971)

    Google Scholar 

  10. Ciarlet, P., Rabier, P.: Les Equations de Von Kárman. Lecture Notes in Math., Nr. 826. Springer-Verlag (1980)

  11. Cimetière A.: Méthode de Galerkin pour flambement de plaques. C. R. Sc. Paris, t. 284, Série A, 1307–1310 (1977)

  12. Cimetière, A.: Flambement unilateral d’une plaque reposant sans frottement sur un support élastique tridimensionnel. C. R. Acad. Sc. Paris, t. 290, Serie B, 337–340 (1980)

  13. Cimetière, A.: Un problème de flambement unilateral en théorie de plaques. J. Mecanique 19(1), 183–202 (1980)

    Google Scholar 

  14. Cimetière, A.: Méthode de Liapounov-Schmidt et branche de bifurcation pour une class d’inéquations variationnelles. C. R. Acad. Sc. Paris, t. 30, Serie (I), Nr. 15, 565–568 (1985)

  15. Cottle R., Pang J., Stone R.: The Linear Complementarity Problem. Academic Press, Boston (1992)

    Google Scholar 

  16. Do, M.C.: Bifurcation theory for elastic plates subjected to unilateral conditions. J. Math. Anal. Appl. 60, 435–448 (1977). doi:10.1016/0022-247X(77)90033-6

    Article  Google Scholar 

  17. Furi, M., Vignoli, A.: A nonlinear spectral approach to surjectivity in Banach spaces. J. Funct. Anal. 20, 304–318 (1975). doi:10.1016/0022-1236(75)90037-3

    Article  Google Scholar 

  18. Giorgieri, E., Väth, M.: A characterization of 0-epi Maps with a Degree. Preprint, University of Rome “Tor Vergata”

  19. Goeleven D., Nguen V.H., Théra M.: Nonlinear eigenvalues problems governed by a variational inequality of Von Kárman’s type: a degree theoretic approach. Topol. Meth. Nonlienar Anal. 2, 253–276 (1993)

    Google Scholar 

  20. Granas, A.: The theory of compact vector fields and some of its applications to topology of functional spaces, (I). Rozpr. Mathematyczne XXX, 1–93 (1962)

  21. Heinz, H.P.: On the behavior of measure of noncompactness with respect to differentiation and integration of vector-valued functions. Nonlinear Anal. 7(12), 1351–1371 (1983). doi:10.1016/0362-546X(83)90006-8

    Article  Google Scholar 

  22. Hyers D.H., Isac G., Rassias T.M.: Topics in Nonlinear Analysis and Applications. World Scientific, Singapore (1997)

    Google Scholar 

  23. Isac G.: Opérateurs asymptotiquement linéaires sur des espaces localement convexes. Colloquium Math. XLVI(1), 67–72 (1982)

    Google Scholar 

  24. Isac, G.: Nonlinear complementarity problem and Galerkin method. J. Math. Anal. Appl. 108(2), 563–575 (1985). doi:10.1016/0022-247X(85)90045-9

    Article  Google Scholar 

  25. Isac,G.: Complementarity Problems. Lecture Notes in Mathematics, Nr. 1528. Springer-Verlag (1992)

  26. Isac, G.: Topological Methods in Complementarity Theory. Kluwer Academic Publishers (2000)

  27. Isac, G.: Leray-Schauder Type Alternatives, Complementarity Problems and Variational Inequalities. Kluwer Academic Publishers (2006)

  28. Isac, G.: Asymptotic Derivable Fields and Nonlinear Complementarity Problems. Preprint (2007)

  29. Isac G., Motreanu D.: On the solvability of complementarity problems and variational inequalities with integral operators. J. Nonlinear Convex Anal. 4(3), 333–351 (2003)

    Google Scholar 

  30. Isac, G., Nemeth, S.Z.: Scalar derivatives and scalar asymptotic derivatives. An Altman type fixed-point theorem on convex cones and some applications. J. Math. Anal. Appl. 290, 452–468 (2004). doi:10.1016/j.jmaa.2003.10.030

    Article  Google Scholar 

  31. Isac, G., Rassias, T.M.: On the Hyers-Ulam stability of ψ-additive mappings. J. Approx. Theory 72(2), 131–137 (1993). doi:10.1006/jath.1993.1010

    Article  Google Scholar 

  32. Krasnoselskii, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations (in Russian), Gostekhizdat, Moscow (1956). Engl. Transl., Macmillan, New York (1964)

  33. Krasnoselskii M.A.: Positive Solutions of Operator Equations. Noordhoff, Groningen (1964)

    Google Scholar 

  34. Le, V.K., Schmitt, K.: Global Bifurcation in Variational Inequalities. Applications to Obstacles and Unilateral Problems. Springer (1997)

  35. Leray J., Schauder J.: Topologie et equations fonctionnelles. Ann. Sc. Ecole. Norm. Sup. 51, 45–78 (1934)

    Google Scholar 

  36. Martelly M., Vignoli A.: Some surjectivity results for non compact multivalued maps. Red. Acad. Sci. Fis. Mater. 41(4), 57–66 (1974)

    Google Scholar 

  37. Mönch, H.: Boundary value problems for nonlinear ordinary differential equations in Banach spaces. Nonlinear Anal. 4(5), 985–999 (1980). doi:10.1016/0362-546X(80)90010-3

    Article  Google Scholar 

  38. Mönch, H., Von Harten, G.F.: On the Cauchy problem for ordinary differential equations in Banach spaces. Arch. Math. Basel 39, 153–160 (1982). doi:10.1007/BF01899196

    Google Scholar 

  39. Petryshyn, W.V.: Remarks on condensing and k-set contractive mappings. J. Math. Anal. Appl. 39, 717–741 (1972). doi:10.1016/0022-247X(72)90194-1

    Article  Google Scholar 

  40. Schechter, M., Shapiro, J., Snow, M.: Solution of the nonlinear problem AU = N(U) in a Banach space. Trans. Am. Math. Soc. 241, 69–78 (1978). doi:10.2307/1998833

    Article  Google Scholar 

  41. Väth M.: Fixed-point theorems and fixed point index for countably condensing maps. Topol. Meth. Nonlinear Anal. 13, 341–363 (1999)

    Google Scholar 

  42. Väth M.: Volterra and Integral Equations of Vector Functions. Marcel Dekker, New York (2000)

    Google Scholar 

  43. Vignoli A.: On qusi-bounded mappings and nonlinear functional equations. Atti. Accad. Naz. Lincei, VIII Ser. Rend. Cl. Sci Fis. Mater. Nat. 50, 114–117 (1971)

    Google Scholar 

  44. Weber V.H.: Φ-Asymptotisches spectrum und surjektivitätssätze vom Fredholm type fur michtlineare operatoren mit anwendungen. Math. Nach. 117, 7–35 (1984)

    Article  Google Scholar 

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Isac, G. Quasi-bounded mappings and complementarity problems depending of parameters. J Glob Optim 47, 355–367 (2010). https://doi.org/10.1007/s10898-008-9350-6

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