On the Solvability of Semilinear Operator Equations and Elliptic Boundary Value Problems
نویسندگان
چکیده
Let L be a bounded linear Fredholm mapping of index zero, mapping a Banach space X into a Banach space 7. Then necessary and sufficient conditions for the solvability of the operator equation Lu = ƒ for ƒ e Y are well known. However the same satisfactory state of affairs does not hold for semilinear operator equations in which a compact nonlinear operator Nu is added to the right hand side of Lu = ƒ. Indeed, most recent approaches to this problem attempt to place enough restrictions on the operator N so that L — N is surjective. A similar state of affairs holds in the case of elliptic boundary value problems defined on bounded domains CI <z R. Recently, however, in the special case of the semilinear Dirichlet problem,
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