On the Palais-Smale condition for Hammerstein integral equations in Hilbert spaces

Abstract

In this paper we deal with nontrivial solvability in balls of Hammerstein integral equations in Hilbert spaces for nonlinearities of potential type. We use a variational approach based on variants of the mountain pass theorem which are due to Guo—Sun-Qi and Schechter. Our main contribution is a new technique to verify compactness conditions of Palais-Smale type. This technique combines the compactness criterium for countable sets in \(L^p\) with basic properties of the measures of noncompactness and integral inequalities.

Authors

Radu Precup
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania

Keywords

Compactness; Hammerstein integral equation; Mountain pass theory.

Paper cordinates

R. Precup, On the Palais-Smale condition for Hammerstein integral equations in Hilbert spaces, Nonlinear  Anal. 47 (2001), 1233-1244. http://dx.doi.org/10.1016/S0362-546X(01)00261-9

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Journal

Nonlinear Analysis

Publisher Name

Elsevier

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Not available yet.

Online ISSN

0362-546X

Google Scholar Profile

Zbl 1042.47530

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