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Multiple solutions for a class of infinitely degenerate elliptic equations with a sign‐changing weight function
Author(s) -
Tian Shuying
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5804
Subject(s) - mathematics , nehari manifold , degenerate energy levels , sign (mathematics) , weight function , mathematical analysis , class (philosophy) , elliptic curve , pure mathematics , function (biology) , sobolev space , dirichlet problem , logarithm , nonlinear system , physics , quantum mechanics , artificial intelligence , evolutionary biology , computer science , biology , boundary value problem
In this paper, we study the Dirichlet problem for a class of degenerate elliptic equations with a sign‐changing weight function. Under some conditions on the weight function, we obtain at least two nontrivial solutions by the method of Nehari manifold and the logarithmic Sobolev inequality.