关键词: 分数阶微分方程, 边值问题, 临界点, p(x)-Laplace算子

Abstract: By using variational methods and the theory of fractional variable exponent Sobolev space, the author investigated the fractional differential equation with p(x)-Laplacian operator, under the condition of local superlinear growth nonlinearity, some sufficient conditions for the existence of multiple solutions for this problem were obtained.

Key words: fractional differential equation, boundary value problem, critical point, p(x)-Laplacian operator