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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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
Akhmerov, R.R., Kamenskii, M.I., Potapov, A.S., Rodkina, A.E., Sadovskii, B.N.: Measures of Noncompactness and Condensing Operators. Birkhäuser Verlag (1992)
Amann, H.: Lecture on Some Fixed Point Theorems, IMPA. Rio de Janeireo-GB (1974)
Ayerbe Toledano, J.M., Dominguez Benavides, T., Lopez Acedo, G.: Measure of Noncompactness in Metric Fixed Point Theory. Birkhäuser Verlag (1997)
Banas, J., Goebel, K.: Measures of Noncompactness in Banach Spaces. Marcel Dekker Inc. (1980)
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
Bourbaki N.: Topologie Générale. Hermann, Paris (1960)
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)
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)
Ciarlet, P., Rabier, P.: Les Equations de Von Kárman. Lecture Notes in Math., Nr. 826. Springer-Verlag (1980)
Cimetière A.: Méthode de Galerkin pour flambement de plaques. C. R. Sc. Paris, t. 284, Série A, 1307–1310 (1977)
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)
Cimetière, A.: Un problème de flambement unilateral en théorie de plaques. J. Mecanique 19(1), 183–202 (1980)
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)
Cottle R., Pang J., Stone R.: The Linear Complementarity Problem. Academic Press, Boston (1992)
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
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
Giorgieri, E., Väth, M.: A characterization of 0-epi Maps with a Degree. Preprint, University of Rome “Tor Vergata”
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)
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)
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
Hyers D.H., Isac G., Rassias T.M.: Topics in Nonlinear Analysis and Applications. World Scientific, Singapore (1997)
Isac G.: Opérateurs asymptotiquement linéaires sur des espaces localement convexes. Colloquium Math. XLVI(1), 67–72 (1982)
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
Isac,G.: Complementarity Problems. Lecture Notes in Mathematics, Nr. 1528. Springer-Verlag (1992)
Isac, G.: Topological Methods in Complementarity Theory. Kluwer Academic Publishers (2000)
Isac, G.: Leray-Schauder Type Alternatives, Complementarity Problems and Variational Inequalities. Kluwer Academic Publishers (2006)
Isac, G.: Asymptotic Derivable Fields and Nonlinear Complementarity Problems. Preprint (2007)
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)
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
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
Krasnoselskii, M.A.: Topological Methods in the Theory of Nonlinear Integral Equations (in Russian), Gostekhizdat, Moscow (1956). Engl. Transl., Macmillan, New York (1964)
Krasnoselskii M.A.: Positive Solutions of Operator Equations. Noordhoff, Groningen (1964)
Le, V.K., Schmitt, K.: Global Bifurcation in Variational Inequalities. Applications to Obstacles and Unilateral Problems. Springer (1997)
Leray J., Schauder J.: Topologie et equations fonctionnelles. Ann. Sc. Ecole. Norm. Sup. 51, 45–78 (1934)
Martelly M., Vignoli A.: Some surjectivity results for non compact multivalued maps. Red. Acad. Sci. Fis. Mater. 41(4), 57–66 (1974)
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
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
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
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
Väth M.: Fixed-point theorems and fixed point index for countably condensing maps. Topol. Meth. Nonlinear Anal. 13, 341–363 (1999)
Väth M.: Volterra and Integral Equations of Vector Functions. Marcel Dekker, New York (2000)
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)
Weber V.H.: Φ-Asymptotisches spectrum und surjektivitätssätze vom Fredholm type fur michtlineare operatoren mit anwendungen. Math. Nach. 117, 7–35 (1984)
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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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DOI: https://doi.org/10.1007/s10898-008-9350-6