Proceedings of the American Mathematical Society

Author(s): Chung-Cheng Kuo
Journal: Proc. Amer. Math. Soc. 124 (1996), 83-87.
MSC (1991): Primary 35J65, 47H11, 47H15
Retrieve article in: PDF
This article is available free of charge

Abstract: We study the existence of solutions of the Neumann problem for semilinear second-order elliptic equations at resonance in which the nonlinear terms may grow superlinearly in one of the directions $u\to\infty$ and $u\to-\infty$ , and sublinearly in the other. Solvability results are obtained under assumptions either with or without a Landesman-Lazer condition. The proofs are based on degree-theoretic arguments.

1: S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math. 12 (1959), 623--727. MR 23:A2610
2: H. Berestycki and D. G. de Figueiredo, Double resonance in semilinear elliptic equations, Comm. Partial Differential Equations. 6 (1981), 91--22. MR 82f:35078
3: C. P. Gupta, Perturbation of second order elliptic problems by unbounded nonlinearities, Nonlinear Anal. 6 (1982), 919--933. MR 84c:35042
4: N. Hirano, Nonlinear perturbations of second order linear elliptic boundary value problems, Houston J. Math. 14 (1988), 105--114. MR 90c:35091
5: R. Iannacci, M. N. Nkashama, and J. R. Ward, Jr., Nonlinear second order elliptic partial differential equations at resonance, Trans. Amer. Math. Soc. 311 (1989), 711--726. MR 90a:35091
6: R. Kannan and R. Ortega, Landesman-Lazer conditions for problems with ``one-side unbounded'' nonlinearities, Nonlinear Anal.9 (1985), 1313--1317. MR 87d:35051
7: E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970), 609--623. MR 42:2171
8: N. G. Lloyd, Degree theory, Cambridge Univ. Press, Cambridge, 1978. MR 58:12558
9: J. R. Ward, Jr., Perturbations with some superlinear growth for a class of second order elliptic boundary value problems, Nonlinear Anal. 6 (1982), 367--374. MR 83i:35076

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35J65, 47H11, 47H15

Chung-Cheng Kuo
Affiliation: Department of Mathematics, Fu Jen University, Taipei, Taiwan

DOI: 10.1090/S0002-9939-96-03145-0
PII: S 0002-9939(96)03145-0
Keywords: Second-order elliptic equation, Landesman-Lazer condition, Leray-Schauder degree
Received by editor(s): June 8, 1994
Additional Notes: This research was supported in part by the National Science Council of the Republic of China
Communicated by: Jeffrey Rauch
Copyright of article: Copyright 1996, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS