Electron. J. Diff. Equ., Vol. 2013 (2013), No. 126, pp. 1-14.

Existence of solutions to second-order boundary-value problems with small perturbations of impulses

Gabriele Bonanno, Beatrice Di Bella, Johnny Henderson

In this article we study second-order impulsive differential equations with Dirichlet boundary conditions, depending on two real parameters. We show that an appropriate growth condition of the nonlinear term, under small perturbations of impulsive terms, ensures the existence of three solutions. The approach is based on variational methods.

Submitted April 4, 2013. Published May 21, 2013.
Math Subject Classifications: 34B37, 34B15, 58E05.
Key Words: Dirichlet boundary condition; impulsive effects; variational methods; critical points.

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Gabriele Bonanno
Department of Civil, Information Technology, Construction,
Environmental Engineering and Applied Mathematics
University of Messina, 98166 - Messina, Italy
email: bonanno@unime.it
Beatrice Di Bella
Department of Mathematics and Computer Science
University of Messina, 98166 - Messina, Italy
email: bdibella@unime.it
Johnny Henderson
Department of Mathematics, Baylor University
Waco, TX 76798-7328, USA
email: Johnny_Henderson@baylor.edu

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