We prove existence results in all of R^N for an elliptic problem of (p,q)-Laplacian type involving a critical term, nonnegative weights and a positive parameter lambda. In particular, under suitable conditions on the exponents of the nonlinearity, we prove existence of infinitely many weak solutions with negative energy when lambda belongs to a certain interval. Our proofs use variational methods and the concentration compactness principle. Towards this aim we give a detailed proof of tight convergence of a suitable sequence.

Multiplicity results for (p,q)-Laplacian equations with critical exponent in R^N and negative energy

Laura Baldelli;Ylenia Brizi;Roberta Filippucci
2021

Abstract

We prove existence results in all of R^N for an elliptic problem of (p,q)-Laplacian type involving a critical term, nonnegative weights and a positive parameter lambda. In particular, under suitable conditions on the exponents of the nonlinearity, we prove existence of infinitely many weak solutions with negative energy when lambda belongs to a certain interval. Our proofs use variational methods and the concentration compactness principle. Towards this aim we give a detailed proof of tight convergence of a suitable sequence.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11391/1475781
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