Abstract
In this article, the equation Au ± B(u) = f is studied in a separable Hilbert space H. Here A: H → H is a linear self-adjoint operator with domain dense in H and B: H → H is nonlinear. It is studied when this equation has a solution for any f ∈ H. The results obtained are applied to the problem of periodic solutions of the nonlinear wave equation with homogeneous boundary conditions of the third kind and to elliptic equations.
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