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Some recent results on the Dirichlet problem for \((p,q)\)-Laplace equations. (English) Zbl 1374.35137

Summary: A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with \((p,q)\)-Laplacian in a bounded domain is performed. Both eigenvalue problems and different types of perturbation terms are briefly discussed. Special attention is paid to possibly coercive, resonant, subcritical, critical, or asymmetric right-hand sides.

MSC:

35J20 Variational methods for second-order elliptic equations
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:

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