Vitali Vougalter, Vitaly Volpert
Existence of solutions for some non-Fredholm integro-differential equations with the bi-Laplacian
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ABSTRACT.  We prove the existence of solutions for some semilinear elliptic equations in the appropriate H^4 spaces using the fixed point technique where the elliptic equation contains fourth order differential operators with and without Fredholm property, generalizing the results of the preceding work [22].