On the Existence in the Sense of Sequences of Stationary Solutions for Some Systems of Non-Fredholm Integro-differential Equations

We prove the existence in the sense of sequences of stationary solutions for some systems of reaction–diffusion type equations in the appropriate H2 spaces. It is established that, under reasonable technical conditions, the convergence in L1 of the integral kernels yields the existence and the convergence in H2 of the solutions. The nonlocal elliptic problems contain the second-order differential operators with and without Fredholm property. © 2018, Springer Nature Switzerland AG.