In this talk, we will introduce a new monotone result to the ground state energy to the scalar field equation. As applications, we use this monotone property to show the existence and concentration behavior of positive ground state solutions and least energy sign-changing solutions for the singularly perturbed elliptic equation with the variable exponent. This is a joint work with Professor Zhi-Qiang Wang and Dr. Yuanze Wu.
学术报告海报.pdf