arXiv subjects
Publications and source records attributed to Hua Jin.
We consider the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the Nehari method in critical point theory, we obtain the existence theorem of ground state solutions for such Dirichlet problem.
Based on the need of studying the fractional boundary value problems by using variational methods, in this paper, we introduce a fundamental theory framework of fractional Sobolev space in one dimension, study the regularity of weak solutions for a fractional boundary value problem with variational structure, give out the spectral structure of operator ${_t}D_T^α{_0}D_t^α$ with Dirichlet boundary value conditions. Especially, when $α=1$, the operator ${_t}D_T^α{_0}D_t^α=-D^2$. So, the results of this paper are the generalization of corresponding conclusions for integer differential operator to some extent.
We focus on the study of $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the genus properties in critical point theory, we establish some new criteria to guarantee the existence of infinitely many weak solutions for the considered problem.