Existence of a nontrivial solution to a strongly indefinite semilinear equation

Authors:
B. Buffoni, L. Jeanjean and C. A. Stuart

Journal:
Proc. Amer. Math. Soc. **119** (1993), 179-186

MSC:
Primary 35J60; Secondary 35Q99, 45K05, 47H15, 47N20

DOI:
https://doi.org/10.1090/S0002-9939-1993-1145940-X

MathSciNet review:
1145940

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Abstract: Under general hypotheses, we prove the existence of a nontrivial solution for the equation , where belongs to a Hilbert space , is an invertible continuous selfadjoint operator, and is superlinear. We are particularly interested in the case where is strongly indefinite and is not compact. We apply the result to the Choquard-Pekar equation

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1145940-X

Keywords:
Semilinear equation,
Choquard-Pekar equation,
strongly indefinite operator,
lack of compactness

Article copyright:
© Copyright 1993
American Mathematical Society