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

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.

Keywords

• Semilinear elliptic equation
• new superlinear conditionl
• general subcritical condition