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Zbl 0958.35052
Ma, To Fu; Sanchez, Luis
Three solutions of a quasilinear elliptic problem near resonance. (English)
[J] Math. Slovaca 47, No.4, 451-457 (1997). ISSN 0139-9918; ISSN 1337-2211/e

Using critical point theory, the authors prove a multiplicity result near the first eigenvalue $\lambda_1$ for quasilinear elliptic problems of the form $$ -\Delta_pu-\lambda_1|u|^{p-2}u+\varepsilon |u|^{p-2}u=f(x,u)+h(x) $$ with Dirichlet conditions. \par It is proved that, for sufficiently small $\varepsilon >0$, the problem above has at least three solutions when $f$ and $h$ satisfy a Landesman-Lazer condition.
[Jean Mawhin (Louvain)]

MSC 2000:: *35J65 (Nonlinear) BVP for (non)linear elliptic equations
58E30 Variational principles on infinite-dimensional spaces
35A15 Variational methods (PDE)
35A05 General existence and uniqueness theorems (PDE)

Keywords: $p$-Laplacian; critical point theory

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