Existence of Weak Solutions for A Class of Nonuniformly Nonlinear Elliptic Equations of $p$-Laplacian Type
The goal of this paper is to study the existence of non-trivial weak solutions for the nonuniformly nonlinear elliptic equation in an unbounded domain. The solution will be obtained in a subspace of the Sobolev space and the proofs rely essentially on a variation of the mountain pass theorem.
Elliptic equations; Mountain pass theorem; Weak solution
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eISSN 0975-8607; pISSN 0976-5905