Given 1<p<N and two measurable functions V(r)≥0 and K(r)>0, r>0, we define the weighted spaces W={u∈D1,p(RN):∫RNV(|x|)|u|pdx<∞},LKq=Lq(RN,K(|x|)dx) and study the compact embeddings of the radial subspace of W into LKqjavax.xml.bind.JAXBElement@46296917+LKqjavax.xml.bind.JAXBElement@a3d56a6, and thus into LKq(=LKq+LKq) as a particular case. We consider exponents q1, q2, q that can be greater or smaller than p. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately. We then apply these results to the investigation of existence and multiplicity of finite energy solutions to nonlinear p-Laplace equations of the form −△pu+V(|x|)|u|p−2u=g(|x|,u)in RN,1<p<N, where V and g(|⋅|,u) with u fixed may be vanishing or unbounded at zero or at infinity. Both the cases of g super and sub p-linear in u are studied and, in the sub p-linear case, nonlinearities with g(|⋅|,0)≠0 are also considered.

Badiale, M., Guida, M., Rolando, S. (2017). Compactness and existence results for the p-Laplace equation. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 451(1), 345-370 [10.1016/j.jmaa.2017.02.011].

Compactness and existence results for the p-Laplace equation

ROLANDO, SERGIO
2017

Abstract

Given 10, r>0, we define the weighted spaces W={u∈D1,p(RN):∫RNV(|x|)|u|pdx<∞},LKq=Lq(RN,K(|x|)dx) and study the compact embeddings of the radial subspace of W into LKqjavax.xml.bind.JAXBElement@46296917+LKqjavax.xml.bind.JAXBElement@a3d56a6, and thus into LKq(=LKq+LKq) as a particular case. We consider exponents q1, q2, q that can be greater or smaller than p. Our results do not require any compatibility between how the potentials V and K behave at the origin and at infinity, and essentially rely on power type estimates of their relative growth, not of the potentials separately. We then apply these results to the investigation of existence and multiplicity of finite energy solutions to nonlinear p-Laplace equations of the form −△pu+V(|x|)|u|p−2u=g(|x|,u)in RN,1
Articolo in rivista - Articolo scientifico
Compact embeddings; Quasilinear elliptic equations with p-Laplacian; Unbounded or decaying potentials; Weighted Sobolev spaces;
Quasilinear elliptic equations with p-Laplacian, unbounded or decaying potentials, weighted Sobolev spaces, compact embeddings
English
345
370
26
Badiale, M., Guida, M., Rolando, S. (2017). Compactness and existence results for the p-Laplace equation. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 451(1), 345-370 [10.1016/j.jmaa.2017.02.011].
Badiale, M; Guida, M; Rolando, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/146647
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