Implicit elliptic boundary-value problems with discontinuous nonlinearities

Set-Valued Analysis

Volumn 4, Issue 3, 1996, Pages 287-300

  Marano, Salvatore A ^a  

^a UNIVERSITY OF CATANIA   (Italy)

Author keywords

Discontinuous nonlinearities; Elliptic differential inclusions; Implicit elliptic equations; Strong solutions

Indexed keywords

EID: 0041296315     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00419370     Document Type: Article

References (18)

1. Adams, R. A.: Sobolev Spaces, Academic Press, New York, 1975.
2. Bielawski, R. and Górniewicz, L.: A fixed point index approach to some differential equations, in: B. Jiang (ed.), Topological Fixed Point Theory and Applications, Lecture Notes in Math. 1411, Springer-Verlag, Berlin, 1989, pp. 9-14.
3. Bielawski, R. and Górniewicz, L.: Some applications of the Leray-Schauder alternative to differential equations, in: S. P. Singh (ed.), Nonlinear Functional Analysis and Its Applications, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 173, Reidel, Dordrecht, 1986, pp. 187-194.
4. Bonanno, G. and Marano, S. A.; Positive solutions of elliptic equations with discontinuous nonlinearities, Topol. Methods Nonlinear Anal. 6 (1996), to appear.
5. Borisovich, Yu. G., Gel'man, B. D., Myshkis, A. D., and Obukhovskii, V. V.: Multivalued mappings, J. Soviet Math. 24 (1984), 719-791.
6. Chang, K. C.: The obstacle problem and partial differential equations with discontinuous nonlinearities, Comm. Pure Appl. Math. 33 (1980), 117-146.
7. Dunford, N. and Schwartz, J. T.: Linear Operators, Part I, Interscience, New York, 1958.
8. Gilbarg, D. and Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order, 2nd edn, Springer-Verlag, Berlin, 1983.
9. Klein, E. and Thompson, A. C.: Theory of Correspondences, Wiley, New York, 1984.
10. Lions. P. L.: Problèmes elliptiques du 2-ème ordre non sous forme divergence, Proc. Royal Soc. Edinburgh Sect. A 84 (1979), 263-271.
11. Marano, S. A.: Existence theorems for a semilinear elliptic boundary value problem, Ann. Polon. Math. 60 (1994), 57-67.
12. Marano, S. A.: Implicit elliptic differential equations, Set-Valued Anal. 2 (1994), 545-558.
13. Marano, S. A.: Elliptic boundary value problems with discontinuous nonlinearities, Set-Valued Anal. 3 (1995), 167-180.
14. Naselli Ricceri, O. and Ricceri, B.: An existence theorem for inclusions of the type ψ(u)(t) ∈ F(t, Φ(u)(t)) and application to a multivalued boundary value problem, Appl. Anal. 38 (1990), 259-270.
15. Pruszko, T.: Some applications of the topological degree theory to multi-valued boundary value problems, Dissertationes Math. 229 (1984), 1-48.
16. Rado, T. and Reichelderfer, P. V.: Continuous Transformations in Analysis, Springer-Verlag, Berlin, 1955.
17. Ricceri, B.: Lipschitzian solutions of the implicit Cauchy problem g(x′) = f(t,x), x(0) = 0, with / discontinuous in x, Rend. Circ. Mat. Palermo (2) 34 (1985), 127-135.
18. Talenti, G.: Elliptic equations and rearrangements, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), 697-718.