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An existence result for \(( p , q )\)-Laplace equations involving sandwich-type and critical growth. (English) Zbl 1445.35183
Summary: We investigate the existence of a nontrivial nonnegative solution to \(( p , q )\)-Laplace equations involving two nonlinear terms, one grows as \(s\) with \(q < s < p\) and the other possibly has critical growth. This interesting case cannot be appeared in single \(m\)-Laplace equations and has not been studied under even the subcritical growth. Our argument is based on the concentration-compactness principle by P. L. Lions and the Ekeland variational principle.
MSC:
35J92 Quasilinear elliptic equations with \(p\)-Laplacian
35J20 Variational methods for second-order elliptic equations
35J25 Boundary value problems for second-order elliptic equations
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