Existence of solutions for impulsive wave equations

Abstract

We study a class of initial value problems for impulsive nonlinear wave equations. A new topological approach is applied to prove the existence of at least one and at least two nonnegative classical solutions. To prove our main results we give a suitable integral representation of the solutions of the considered problem. Then, we construct two operators so that any fixed point of their sum is a solution.

Keywords

• wave equations
• impulsive wave equations
• positive solution
• fixed point
• cone
• sum of operators