A two-point boundary value problem with jumping nonlinearities

Castro B., Alfonso

doi:10.1090/S0002-9939-1980-0565340-1

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 $u'' + u = \alpha {u^ - } + p(t),u(0) = 0 = u(\pi )$ , 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.