Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝ<sup>N</sup>

Alves, Claudianor O.; dos Santos, Alan C.B.

doi:10.1051/cocv/2017045

Geodesic

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Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝ^N

Alves, Claudianor O.¹ ; dos Santos, Alan C.B.¹

ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1231-1248

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Résumé

In this paper, we establish existence and multiplicity of solutions for the following class of quasilinear field equation $- Δ u + V (x) u - Δ_{p} u + W' (u) = 0, ℝ^{N},$

where $u = (u_{1}, u_{2}, ..., u_{N + 1}), p > N \geq 2, W$ is a singular function and $V$ is a positive continuous function.

MR Zbl

DOI : 10.1051/cocv/2017045

Classification : 35J60, 35A15
Keywords: Nonlinear elliptic equations, variational methods

Affiliations des auteurs :

Alves, Claudianor O. ¹ ; dos Santos, Alan C.B. ¹

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     author = {Alves, Claudianor O. and dos Santos, Alan C.B.},
     title = {Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on {\ensuremath{\mathbb{R}}\protect\textsuperscript{N}}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1231--1248},
     publisher = {EDP-Sciences},
     volume = {24},
     number = {3},
     year = {2018},
     doi = {10.1051/cocv/2017045},
     zbl = {1410.35049},
     mrnumber = {3877200},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2017045/}
}

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Alves, Claudianor O.; dos Santos, Alan C.B. Existence and multiplicity of solutions for a class of quasilinear elliptic field equation on ℝ^N. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 3, pp. 1231-1248. doi: 10.1051/cocv/2017045

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