ArticleOriginal scientific text
Title
A note on solutions of semilinear equations at resonance in a cone
Authors 1
Affiliations
- Institute of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Abstract
A connection between the Landesman-Lazer condition and the solvability of the equation Lx = N(x) in a cone with a noninvertible linear operator L is studied. The result is based on the abstract framework from [5], applied to the existence of periodic solutions of ordinary differential equations, and compared with theorems by Santanilla (see [7]).
Keywords
nonnegative solutions, equations at resonance
Bibliography
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- E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609-623.
- J. L. Mawhin, Topological degree methods in nonlinear boundary value problems, CBMS Regional Conf. Ser. in Math. 40, Amer. Math. Soc., Providence, R.I., 1979.
- B. Przeradzki, An abstract version of the resonance theorem, Ann. Polon. Math. 53 (1991), 35-43.
- B. Przeradzki, Operator equations at resonance with unbounded nonlinearities, preprint.
- B. Przeradzki, A new continuation method for the study of nonlinear equations at resonance, J. Math. Anal. Appl., to appear.
- J. Santanilla, Nonnegative solutions to boundary value problems for nonlinear first and second order ordinary differential equations, ibid. 126 (1987), 397-408.
- J. Santanilla, Existence of nonnegative solutions of a semilinear equation at resonance with linear growth, Proc. Amer. Math. Soc. 105 (1989), 963-971.
- S. A. Williams, A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem, J. Differential Equations 8 (1970), 580-586.
Pages:
95-103
Main language of publication
English
Received
1992-06-17
Published
1993
Exact and natural sciences