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A pair of positive solutions for $(p,q)$-equations with combined nonlinearities

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  • We consider a parametric nonlinear Dirichlet problem driven by the $(p,q)$-differential operator, with a reaction consisting of a ``concave'' term perturbed by a $(p-1)$-superlinear perturbation, which need not satisfy the Ambrosetti-Rabinowitz condition (problem with combined or competing nonlinearities). Using variational methods we show that for small values of the parameter the problem has at least two nontrivial positive smooth solutions.
    Mathematics Subject Classification: Primary: 35J20; Secondary: 35J60, 35J92.

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