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 \(\Delta\), and more generally for the \(p\)-Laplacian \(\Delta_p\). This spectrum is completely characterized in the linear case of the Laplacian. As an application, we study the existence of solution in \(W^{1,p}_0(\Omega)\) of the equation \(-\Delta_pu= f(x,u,\nabla u)+ h(x)\), when the function \(f\) satisfies some nonresonance condition with respect to that spectrum.


35P05 General topics in linear spectral theory for PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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