Electron. J. Differential Equations, Vol. 2018 (2018), No. 88, pp. 1-17.

Existence and multiplicity of solutions to semilinear elliptic equation with nonlinear term of superlinear and subcritical growth

Xiao-Feng Ke, Chun-Lei Tang

Abstract:
This article concerns the existence and multiplicity of solutions to the superlinear elliptic problems. We introduce a new superlinear condition which is proved to be weaker than the Ambrosetti-Rabinowitz condition, the nonquadratic condition, the monotonicity conditions. As an application, positive solution and infinitely many solutions to semilinear elliptic equation with general subcritical growth are obtained, which generalize some known results.

Submitted February 4, 2018. Published April 10, 2018.
Math Subject Classifications: 35J20, 35J61, 35D30.
Key Words: Semilinear elliptic equation; new superlinear conditionl; general subcritical condition.

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Xiao-Feng Ke
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: kexf@swu.edu.cn
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: tangcl@swu.edu.cn

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