A two-point boundary value problem with jumping nonlinearities
Author:
Alfonso Castro B.
Journal:
Proc. Amer. Math. Soc. 79 (1980), 207-211
MSC:
Primary 34B10
DOI:
https://doi.org/10.1090/S0002-9939-1980-0565340-1
MathSciNet review:
565340
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that a certain two point BVP with jumping nonlinearities has a solution. Our result generalizes that of [2]. We use variational methods which permit giving a minimax characterization of the solution. Our proof exposes the similarities between the variational behavior of this problem and that of other semilinear problems with noninvertible linear part (see [5]).
- [1] R. Adams, Sobolev spaces, Academic Press, New York, 1975. MR 0450957 (56:9247)
- [2]
L. Aguinaldo and K. Schmitt, On the boundary value problem
, Proc. Amer. Math. Soc. 68 (1978), 64-68. MR 0466707 (57:6584)
- [3] S. Ahmad, A. C. Lazer and J. Paul, Elementary critical point theory and perturbations of elliptic boundary value problems at resonance, Indiana Univ. Math. J. 25 (1976), 933-944. MR 0427825 (55:855)
- [4] S. Fucik, Boundary value problems with jumping nonlinearities, Časopis Pěst. Mat. 101 (1976), 69-87. MR 0447688 (56:5998)
- [5] P. Rabinowitz, Some minimax theorems and applications to nonlinear partial differential equations, M. R. C. Technical Report # 1633, 1976.
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34B10
Retrieve articles in all journals with MSC: 34B10
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1980-0565340-1
Keywords:
Critical point,
weak solution,
jumping nonlinearities
Article copyright:
© Copyright 1980
American Mathematical Society