Existence and Multiplicity Results for a Non Linear Hammerstein Integral Equation
In this paper we study the solvability of a nonlinear Hammerstein integral equation by using a variational principle of B. Ricceri and methods of critical point theory. In particular we do not require any positivity assumption on the kernel of the equation. Our results can be applied to higher order elliptic boundary value problem with changing sign kernel.
Unable to display preview. Download preview PDF.
- G. Anello, G. Cordaro, An existence and localization theorem for the solutions of a Dirichlet problem, Ann. Polon. Math., to appear.Google Scholar
- V. Kozlov, V. Maz’ya, J. Rossmann, Elliptic boundary value problems in domain with point singularities. Mathematical Surveys and Monographs, Vol. 52, A.M.S., 1997.Google Scholar
- M.A. Krasnoselskii, Topological methods in the theory of non-linear integral equations. Macmillan, New York, 1964.Google Scholar
- A. Povolotskii, P. Zabreiko, On the theory of Hammerstein equations (Russian). Ukrain. Mat. Zh. 22 (1970), 150–162.Google Scholar
- P.H. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. in Math, 65 A.M.S., R.I., 1986.Google Scholar
- P. Zabreiko, On the theory of Integral Operators (Russian), Thesis, Voronej State University, 1968.Google Scholar