Posts by Radu Precup

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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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

References

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[8] V. Moroz, A. Vignoli, P. Zabvreiko,  On the three critical points theorem,  Topol. Methods Nonlinear Anal. 11, 103-113, 1998.
[9] V.B.Moroz, P.P. Zabreiko,  A variant of the mountain pass theorem and its application to Hammerstein integral equations,  Zeit. Anal. Anwendungen 15, 985-997, 1996.
[10] D. O’Regan, R. Precup,  Existence criteria for integral equations in Banasch spaces, J. Inequal. Appl., to appear.
[11] R. Precup, Nonlinear integral equations (In Romanian), University Babes-Bolyai, Cluj, 1993.
[12] R. Precup, Nontrivial solvability of Hammerstein integral equations in Hilbert spaces,  Seminaire de la theorie de la meilleure approximation, convexite et optimisation, Srima, Cluj-Napoca, 255-265, 2000.
[13] M. Schechter,  A bounded mountain pass lemma without the (PS) condition and applciations,  Trans. Amer. Math. Soc., 331, 681-703, 1992.

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