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
About this paper
Cite this paper as:
Journal
Nonlinear Analysis
Publisher Name
Elsevier
Print ISSN
Not available yet.
Online ISSN
0362-546X
Google Scholar Profile
Zbl 1042.47530
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