Existence and Multiplicity of Solutions for a Class of Semilinear Elliptic Equations

Abstract

The existence and multiplicity results are obtained for solutions of a class of the Dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods, respectively.

Remarks on existence and multiplicity of solutions for a class of semilinear elliptic equations

“…(10) and (11) are weaker than (4). There are functions f (x, t) and h(x) satisfying our Theorem 1 and not satisfying those in [1][2][3][4][5][6][8][9][10][11][12][13][14][15][16][17][18][19]23]. In fact, let…”

“…Recently, the following existence theorem in the critical growth case and multiplicity result in the subcritical growth case are obtained in [5].…”

“…x ∈ Ω is considered by many authors (see [1][2][3][4][5] and the references therein). The existence results are given for problem (1) in [1][2][3][4][5][9][10][11][12][13][14][15][16][17][18][19]23].…”

“…The existence results are given for problem (1) in [1][2][3][4][5][9][10][11][12][13][14][15][16][17][18][19]23]. In [5][6][7][8] some multiplicity theorems are obtained by using the topological degree technique and the variational methods, respectively. Except for [1,2,23], the linear case is only treated.…”

On multiplicity of solutions of Dirichlet problem for uniformly elliptic operator equations

“…x ∈ Ω, Liu and Tang [7] and Liu, Tang and Wu [8] studied the existence of single-solution and two nonzero solutions of problem (1.1), their results generalized and improved corresponding results in [3,5]; for the cases…”