arXiv subjects

Chunhua Wang

Publications and source records attributed to Chunhua Wang.

24 records · Page 2Linked to original sources

arXiv2015

Infinitely many solutions for a nonlinear Schrödinger equation with non-symmetric electromagnetic fields

In this paper, we study the nonlinear Schrödinger equation with non-symmetric electromagnetic fields $$\Big(\frac{\nabla}{i}-A_ε x)\Big)^2 u+V_ε(x)u=f(u),\ u\in H^1 (\mathbb{R}^N,\mathbb{C}), $$ where $A_ε(x)=(A_{ε,1}(x),A_{ε,2}(x),\cdots,A_{ε,N}(x))$ is a magnetic field satisfying that $A_{ε,j}(x)(j=1,\ldots,N)$ is a real $C^{1}$ bounded function on $\mathbb{R}^{N}$ and $V_ε(x)$ is an electric potential. Both of them satisfy some decay conditions and $f(u)$ is a nonlinearity satisfying some nondegeneracy condition. Applying localized energy method, we prove that there exists some $ε_{0 }> 0$ such that for $0 < ε< ε_{0 }$, the above problem has infinitely many complex-valued solutions.

math.AP↗

arXiv2015

Infinitely many solutions to linearly coupled Schrödinger equations with non-symmetric potential

We study a linearly coupled Schrödinger system in $\R^N(N\leq3).$ Assume that the potentials in the system are continuous functions satisfying suitable decay assumptions, but without any symmetry properties and the parameters in the system satisfy some suitable restrictions. Using the Liapunov-Schmidt reduction methods two times and combing localized energy method, we prove that the problem has infinitely many positive synchronized solutions, which extends the result Theorem 1.2 about nonlinearly coupled Schrödinger equations in \cite{aw} to our linearly coupled problem.

math-ph↗

arXiv2015

Infinitely many sign-changing solutions for an elliptic problem with double critical Hardy-Sobolev-Maz'ya terms

In this paper, we investigate the following elliptic problem involving double critical Hardy-Sobolev-Maz'ya terms: $$ \left\{\begin{array}{ll} -Δu = μ\frac{|u|^{2^*(t)-2}u}{|y|^t} + \frac{|u|^{2^*(s)-2}u}{|y|^s} + a(x) u, & {\rm in}\ Ω,\\ \quad u = 0, \,\, &{\rm on}\ \partial Ω, \end{array} \right. $$ where $μ\geq0$, $a(x)>0$, $2^*(t)=\frac{2(N-t)}{N-2}$, $2^*(s) = \frac{2(N-s)}{N-2}$, $0\leq t 6+t$ when $μ>0,$ and $N>6+s$ when $μ=0,$ and $Ω$ satisfies some geometric conditions, then the above problem has infinitely many sign-changing solutions. The main tool is to estimate Morse indices of these nodal solution.

math.AP↗

arXiv2015

On modules for double affine Lie algebras

Imaginary Verma modules, parabolic imaginary Verma modules, and Verma modules at level zero for double affine Lie algebras are constructed using three different triangular decompositions. Their relations are investigated, and several results are generalized from the affine Lie algebras. In particular, imaginary highest weight modules, integrable modules, and irreducibility criterion are also studied.

math.RT↗

arXiv2015

Infinitely many solutions for p-Laplacian equation involving double critical terms and boundary geometry

Let $1 p^{2}+p,a(0)>0$ and $Ω$ satisfies some geometry conditions if $0\in\partialΩ$, say, all the principle curvatures of $\partialΩ$ at $0$ are negative, then the above problem has infinitely many solutions.

math.AP↗

arXiv2014

NODAL Vector solutions with clustered peaks for a nonlinear elliptic equations in $\R^3$

In this paper, we study the following coupled nonlinear Schrödinger system in $\R^3$ $$ \left\{% \begin{array}{ll} -ε^2Δu +P(x)u=μ_1 u^3+βv^2u,~~&x\in \R^3,\vspace{0.15cm}\\ -ε^2Δv +Q(x)v=μ_2 v^3+βu^2v,~~&x\in \R^3,\\ \end{array}% \right. $$ where $μ_1 >0,μ_2>0$ and $β\in \R$ is a coupling constant. Whether the system is repulsive or attractive, we prove that it has nodal semi-classical segregated or synchronized bound states with clustered spikes for sufficiently small $ε$ under some additional conditions on $P(x), Q(x)$ and $β$. Moreover, the number of this type of solutions will go to infinity as $ε\to 0^+$.

math-ph↗