The Coefficient Functions Affect the Existence of Multiple Solutions for the P(X)-Laplacian Equations

In this project, we will investigate the existence of multiple solutions of the following problem: where is a bounded domain with smooth boundary and Let K:[0, )-＞ R be a nondecreasing continuous function, and f,g: be two Caratheodory functions with a subcritical growth. Moreover, consider we would like to study the methods of Tarantello’s paper to improve our results. Let be the space with the norm The variable exponent Lebesgue space is defined by with the norm The space is the closure of in . A weak solution u of this problem is defined that satisfies for all Associated with this problem, we consider the functional Besides, It is related to the stationary version of the Kirchhoff type equation

Project ID:PA10607-0825
External Project ID:MOST106-2115-M182-001