publication . Other literature type . Article . 1972

On the solvability of semilinear operator equations and elliptic boundary value problems

Melvyn S. Berger; Martin Schechter;
Open Access English
  • Published: 01 Sep 1972
  • Publisher: American Mathematical Society
Abstract
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,...
Subjects
free text keywords: 47H15, 35J60, Compact operator, Trace operator, Elliptic boundary value problem, Poincaré–Steklov operator, Elliptic operator, Mathematical analysis, Hypoelliptic operator, Semi-elliptic operator, Mathematics, p-Laplacian
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publication . Other literature type . Article . 1972

On the solvability of semilinear operator equations and elliptic boundary value problems

Melvyn S. Berger; Martin Schechter;