Theorem about existence and uniqueness of continuous solution of nonlocal problem for nonlinear hyperbolic equation

Abstract

The aim of the paper is to give a theorem about the existence and uniqueness of the continuous solution of a non-linear differential hyperbolic problem with a nonlocal condition in a bounded domain. The Banach theorem about the fixed point is used to prove the existence and uniqueness of the problem considered. The results obtained in this paper can be applied in the theory of elasticity with better effect than the analogous known result with the classical initial condition.

AMS(MOS:

• 35L70
• 35L20
• 35L10
• 35L99
• 58C30
• 47H10

Keywords:

• Nonlinear hyperbolic problem
• nonlocal condition
• integral equations
• existence and uniqueness of the solution
• Banach theorem