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Higher order spectrum and problems of non-resonance. (Spectre d’ordre supérieur et problèmes de non-résonance.) (French) Zbl 0880.35083
Summary: We introduce a “higher order” spectrum for the Laplacian Δ, and more generally for the p-Laplacian Δ p . This spectrum is completely characterized in the linear case of the Laplacian. As an application, we study the existence of solution in W 0 1,p (Ω) of the equation -Δ p u=f(x,u,u)+h(x), when the function f satisfies some nonresonance condition with respect to that spectrum.
MSC:
35P05General topics in linear spectral theory of PDE
35J65Nonlinear boundary value problems for linear elliptic equations
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation