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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.
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