Posts by Radu Precup


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.


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


Compactness; Hammerstein integral equation; Mountain pass theory.

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R. Precup, On the Palais-Smale condition for Hammerstein integral equations in Hilbert spaces, Nonlinear  Anal. 47 (2001), 1233-1244.


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Nonlinear Analysis

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Zbl 1042.47530


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