Global existence of solutions to some semilinear integro-differential evolution equations with sign-varying kernels

Abstract

In this paper, we study the global existence of solutions to some semilinear integro-differential evolution equations in Hilbert spaces with sign-varying kernels. By treating the problem through fixed point theory and energy method, we obtain the global existence theorem on [0, +∞) of mild and strong solution to the evolution equations with memory effects for oscillating and sign-varying kernels. This theorem generalizes and improves some previous existence results.

Keywords

• energy method
• integro-differential evolution equation
• global existence
• hilbert spaces
• sign-varying kernels
• 45g05
• 45n05
• 45k05
• 34g20
• 35l90
• 35b35
• 35q74