Ground states of Schrödinger systems with Chern-Simons gauge fields
We are concerned with the study of existence of nontrivial ground states solutions for of Schrödinger systems with Chern-Simons gauge fields.
math.AP↗
arXiv subjects
Taiyong Chen
Publications and source records attributed to Taiyong Chen.
Semiclassical states for coupled nonlinear Schrödinger equations with a critical frequency
In this paper, we are concerned with the coupled nonlinear Schrödinger system \begin{align*} \begin{cases} -\varepsilon^{2}Δu+a(x)u=μ_{1}u^{3}+βv^{2}u \ \ \ \ \mbox{in}\ \mathbb{R}^{N},\\ -\varepsilon^{2}Δv+b(x)v=μ_{2}v^{3}+βu^{2}v \ \ \ \ \ \mbox{in}\ \mathbb{R}^{N}, \end{cases} \end{align*} where $1\leq N\leq3$, $μ_{1},μ_{2},β>0$, $a(x)$ and $b(x)$ are nonnegative continuous potentials, and $\varepsilon>0$ is a small parameter. We show the existence of positive ground state solutions for the system above and also establish the concentration behaviour as $\varepsilon\rightarrow0$, when $a(x)$ and $b(x)$ achieve 0 with a homogeneous behaviour or vanish in some nonempty open set with smooth boundary.
math.AP↗
Existence and Multiplicity of Nontrivial Weak Solutions for Kirchhoff-type Fractional $p$-Laplacian Equation
We discuss the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the mountain pass theorem and the genus properties in critical point theory, we get some new results on the existence and multiplicity of nontrivial weak solutions for such Dirichlet problem.
math.CA↗
Ground State Solutions of Kirchhoff-type Fractional Dirichlet Problem with $p$-Laplacian
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.
math.CA↗
Fractional Sobolev Space and Spectral Structure of Fractional Dirichlet Boundary Value 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.
math.SP↗
Infinitely Many Weak Solutions for Fractional Dirichlet Problem with $p$-Laplacian
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.
math.CA↗