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.
Highlights
The theory of impulsive boundary value problems (IBVPs) became an important area of studies in recent years
IBVPs appear in mathematical models of processes with sudden changes in their states
Some classical tools used in the study of impulsive differential equations are topological methods as fixed point theorems, monotone iterations, upper and lower solutions
Summary
The theory of impulsive boundary value problems (IBVPs) became an important area of studies in recent years. We will prove the following existence result for p > . Having in mind the case < p < , we introduce the following condition: (H ) There exist positive constants Aj, Bj, j = , . N such that the functions Gj, Hj, defined in ( ), satisfy the conditions
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