Existence of nontrivial solution for Schrdinger equations with Hatree and Logarithmic nonlinearities

Abstract

In order to expound the influence of sign-changing potential on logarithmic nonlinearity and Hatree nonlinearity. By the variational method, a weak solution to the problem is a critical point of the energy functional. Then, by the logarithmic inequality, the energy functional of Schrdinger problem satisfies the mountain geometry and (PS) condition. The existence of nontrivial solutions is obtained by mountain pass theorem. The research method has good expected results in theoretical proof and laid a good foundation for the study of Schrdinger problem with logarithmic nonlinearity with double sign-changing potential.

Keywords

• nonlinear functional analysis
• schrdinger equation
• sign-changing potential
• logarithmic inequality
• variational method
• nontrivial solution