Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-12T06:12:51.748Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiplicity results for a nonlinear Dirichlet problem

Published online by Cambridge University Press:  14 November 2011

S. Solimini
S. Solimini
Affiliation:
International School for Advanced Studies(ISAS), Trieste, Italy
Get access Rights & Permissions [Opens in a new window]

Synopsis

This paper deals with some multiplicity results for elliptic problems with jumping nonlinearities. Our results are concerned with the case in which only one eigenvalue of the linear problem is jumped and it is simple. The main tool used is the Leray–Schauder topological degree. We consider a parametrized problem and prove the existence of two or three distinct solutions for suitable values of the parameter.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 3-4 , 1984 , pp. 331 - 336
Copyright
Copyright © Royal Society of Edinburgh 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Amann, H. and Hess, P.. A multiplicity result for a class of elliptic boundary value problems. Proc. Roy. Soc. Edinburgh Sect, A 84 (1979), 145–151.CrossRefGoogle Scholar
2Ambrosetti, A.. Elliptic equations with jumping nonlinearities. J. Math. Phys. Sci. to appear.Google Scholar
3Dancer, E. N.. On the ranges of certain weakly nonlinear partial differential equations. J. Math. Pures Appl. 57 (1978), 351–366.Google Scholar
4Gallouet, T. and Kavian, O.. Resultats d'existence et de nonexistence de solutions pour certains problemes demi-lineaires a l'infini. Ann. Fac. Sci. Toulouse (1981).CrossRefGoogle Scholar
5Hofer, H.. Variational and topological methods in partially ordered Hilbert spaces. Math. Ann. 61 (1982), 493–514.CrossRefGoogle Scholar
6Kazdan, J. L. and Warner, F. W.. Remarks on some quasilinear elliptic equations. Comm. Pure Appl. Math. 28 (1975), 567–597.CrossRefGoogle Scholar
7Lazer, A. C. and McKenna, P. J.. On the number of solutions of a nonlinear Dirichlet problem. J. Math. Anal. Appl. 84 (1981), 282–294.CrossRefGoogle Scholar
8Ruf, B.. On nonlinear elliptic problems with jumping nonlinearities. Ann. Mat. Pura Appl. (IV) 128 (1981), 133–151.CrossRefGoogle Scholar
9Solimini, S.. Existence of a third solution for a class of b.v.p. with jumping nonlinearities. Nonlinear Anal. TMA 7 (8) (1983), 917–927.CrossRefGoogle Scholar
10Lazer, A. C. and McKenna, P. J.. Some multiplicity results for a class of semilinear elliptic and parabolic boundary value problems. J. Math. Anal. Appl. to appear.Google Scholar
11Lazer, A. C. and McKenna, P. J.. Multiplicity results for a semilinear boundary value problem with the nonlinearity crossing higher eigenvalues, preprint.Google Scholar