Existence in the Sense of Sequences of Stationary Solutions for Some Non-Fredholm Integro-Differential Equations

Abstract

We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in appropriate H² spaces. It is shown that, under reasonable technical conditions, the convergence in L¹ of the integral kernels implies the existence and convergence in H² of solutions. The nonlocal elliptic equations involve second order differential operators with and without the Fredholm property. Bibliography: 21 titles.