Vitali Vougalter, Vitaly Volpert
Existence in the sense of sequences of stationary solutions for some non-Fredholm integro-differential equations
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ABSTRACT. We establish the existence in the sense of sequences of stationary solutions for some reaction-diffusion type equations in the appropriate
H^2 spaces. It is shown that under reasonable technical conditions the convergence in L^1 of the integral kernels implies the existence and the convergence in H^2 of the solutions. The nonlocal elliptic equations involve second order differential operators with and without Fredholm property.