Second order evolution equations with nonlocal conditions

Abstract

In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.

Keywords

• Second order differential equations
• mild solution
• evolution system
• Fréchet space
• nonlocal condition
• Hausdorff’s measures of noncompactness
• 34G20