On existence and concentration of solutions to a class of quasilinear problems involving the 1-Laplace operator View Full Text


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Article Info

DATE

2017-09-30

AUTHORS

Claudianor O. Alves, Marcos T. O. Pimenta

ABSTRACT

In this work we use variational methods to prove results on existence and concentration of solutions to a problem in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^N$$\end{document} involving the 1-Laplacian operator. A thorough analysis on the energy functional defined in the space of functions of bounded variation BV(RN)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BV(\mathbb {R}^N)$$\end{document} is necessary, where the lack of compactness is overcome by using the Concentration of Compactness Principle due to Lions. More... »

PAGES

143

References to SciGraph publications

  • 1996-02. Local mountain passes for semilinear elliptic problems in unbounded domains in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1984. Minimal Surfaces and Functions of Bounded Variation in NONE
  • 1993-04. On concentration of positive bound states of nonlinear Schrödinger equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1997-12. Semiclassical States of Nonlinear Schrödinger Equations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2009-06-03. Linking solutions for quasilinear equations at critical growth involving the “1-Laplace” operator in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 1990-07. On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1992-03. On a class of nonlinear Schrödinger equations in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
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    http://scigraph.springernature.com/pub.10.1007/s00526-017-1236-3

    DOI

    http://dx.doi.org/10.1007/s00526-017-1236-3

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