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Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations

Alberto Cabada1* and Stepan Tersian2

Author Affiliations

1 Departamento de Análise Matemática, Facultade de Matemáticas, Universitade de Santiago de Compostela, Santiago de Compostela, Spain

2 Department of Mathematics, University of Ruse, Ruse, 7017, Bulgaria

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Boundary Value Problems 2014, 2014:105  doi:10.1186/1687-2770-2014-105


Dedicated to Professor Ivan Kiguradze for his merits in the mathematical sciences

Published: 8 May 2014

Abstract

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke’s theorems.

MSC: 34B15, 34B37, 58E30.

Keywords:
fourth-order differential equations; impulsive conditions; weak solution; classical solution; Palais-Smale condition; mountain-pass theorem; Clarke’s theorem