Volume 35, Issue 4
A Note on Existence of a Bound State for a Non-Autonomous Nonlinear Scalar Field Equation

Anal. Theory Appl., 35 (2019), pp. 355-376.

Published online: 2020-01

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• Abstract

The aim of this paper is to present a positive solution of a semilinear elliptic equation in $\mathbb{R}^{N}$ with non-autonomous non-linearities which are not necessarily pure-powers, nor homogeneous, and which are superlinear or asymptotically linear at infinity. The proof is variational combined with topological arguments.

• Keywords

Schrödinger equation, asymptotically linear, superlinear, variational methods.

35Q55, 35B09, 35J20

lilimaia@unb.br (Liliane A. Maia)

elson.moura@ufvjm.edu.br (Elson L. Moura)

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@Article{ATA-35-355, author = {Liliane A. and Maia and lilimaia@unb.br and 6440 and Departamento de Matem´atica, Universidade de Bras´ılia, 70910-900 Brasilia, Brazil and Liliane A. Maia and Elson L. and Moura and elson.moura@ufvjm.edu.br and 6441 and Universidade Federal dos Vales do Jequitinhonha e Mucuri, 39803-371 Te´ofilo Otoni-MG, Brazil and Elson L. Moura}, title = {A Note on Existence of a Bound State for a Non-Autonomous Nonlinear Scalar Field Equation}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {35}, number = {4}, pages = {355--376}, abstract = {

The aim of this paper is to present a positive solution of a semilinear elliptic equation in $\mathbb{R}^{N}$ with non-autonomous non-linearities which are not necessarily pure-powers, nor homogeneous, and which are superlinear or asymptotically linear at infinity. The proof is variational combined with topological arguments.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0014}, url = {http://global-sci.org/intro/article_detail/ata/13617.html} }
TY - JOUR T1 - A Note on Existence of a Bound State for a Non-Autonomous Nonlinear Scalar Field Equation AU - Maia , Liliane A. AU - Moura , Elson L. JO - Analysis in Theory and Applications VL - 4 SP - 355 EP - 376 PY - 2020 DA - 2020/01 SN - 35 DO - http://doi.org/10.4208/ata.OA-0014 UR - https://global-sci.org/intro/article_detail/ata/13617.html KW - Schrödinger equation, asymptotically linear, superlinear, variational methods. AB -

The aim of this paper is to present a positive solution of a semilinear elliptic equation in $\mathbb{R}^{N}$ with non-autonomous non-linearities which are not necessarily pure-powers, nor homogeneous, and which are superlinear or asymptotically linear at infinity. The proof is variational combined with topological arguments.

Liliane A. Maia & Elson L. Moura. (2020). A Note on Existence of a Bound State for a Non-Autonomous Nonlinear Scalar Field Equation. Analysis in Theory and Applications. 35 (4). 355-376. doi:10.4208/ata.OA-0014
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