相关论文: Entire sign-changing solutions to the fractional c…

We study dynamical properties of blowup solutions to the focusing $L^2$-supercritical nonlinear fractional Schr\"odinger equation \[ i\partial_t u -(-\Delta)^s u = -|u|^\alpha u, \quad u(0) = u_0, \quad \text{on } [0,\infty) \times…

We study a competitive nonlinear Schr\"odinger system in $\mathbb{R}^N$ whose nonlinear potential is localized in small regions that shrink to isolated points. Within a variational framework based on a fully sign-changing Nehari constraint…

In this paper we are concerned with the existence and multiplicity of solutions for the fractional Choquard-type Schr\"{o}dinger-Kirchhoff equations with electromagnetic fields and critical nonlinearity: \begin{eqnarray*} \begin{cases}…

We study the following coupled Schr\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {cases}-\Delta u_1 +\la_1 u_1 = \mu_1 u_1^3+\beta u_1 u_2^2, \quad x\in \Omega, -\Delta u_2 +\la_2 u_2…

This paper is concerned with the following fractional Schr\"{o}dinger equations involving critical exponents: \begin{eqnarray*} (-\Delta)^{\alpha}u+V(x)u=k(x)f(u)+\lambda|u|^{2_{\alpha}^{*}-2}u\quad\quad \mbox{in}\ \mathbb{R}^{N},…

In the present paper we consider the coupled system of nonlinear Schr\"{o}dinger equations with the fractional Laplacian \[ \left\{ \begin{aligned} (-\Delta)^\alpha u_1 & = \lambda_1u_1+f_1(u_1)+\partial_1F(u_1,u_2)\ \ \mathrm{in}\…

This paper is concerned with the following fractional Schr\"odinger equation \begin{equation*} \left\{ \begin{array}{ll} (-\Delta)^{s} u+u= k(x)f(u)+h(x) \mbox{ in } \mathbb{R}^{N}\\ u\in H^{s}(\R^{N}), \, u>0 \mbox{ in } \mathbb{R}^{N},…

In this paper we consider the following class of fractional Kirchhoff equations with critical growth: \begin{equation*} \left\{ \begin{array}{ll}…

In this paper, we study the concentration and multiplicity of solutions to the following fractional Schr\"{o}dinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} \varepsilon^{2s}(-\Delta)^su+V(x)u+\phi u=f(u)+u^{2_s^{\ast}-1} &…

In this paper, we study the existence of multiple positive solutions for a class of fractional Schr\"{o}dinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. With the help of Nehari…

In this paper, we study the fractional critical Schr\"{o}dinger-Poisson system \[\begin{cases} (-\Delta)^su +\lambda\phi u= \alpha u+\mu|u|^{q-2}u+|u|^{2^*_s-2}u,&~~ \mbox{in}~{\mathbb R}^3,\\ (-\Delta)^t\phi=u^2,&~~ \mbox{in}~{\mathbb…

In this paper, we study the existence of localized sign-changing (or nodal) solutions for the following nonlinear Schr\"odinger-Poisson system \begin{equation*} \begin{cases} -\varepsilon^2 \Delta u+V(x)u+\phi…

We study the Choquard equation involving mixed local and nonlocal operators $$-\Delta u+(-\Delta)^{s}u+V(x)u=(\frac{1}{|x|^{\mu}}* F(u))f(u)\quad\text{in }\R^{2},$$ where $s\in(0,1)$, $\mu\in(0,2)$, $F(t)=\int_{0}^{t} f(\tau)\,d\tau$, and…

In this paper, we study the fractional Schr\"{o}dinger-Poisson equation \begin{equation*} \ \left\{\begin{aligned} &(-\Delta)^{s}u+V(x)u+K(x)\phi u=|u|^{2^{\ast}_{s}-2}u, &\mbox{in} \ \mathbb{R}^{3},\\…

We consider the following critical semilinear nonlocal equation involving the fractional Laplacian $$ (-\Delta)^su=K(|x|)|u|^{2^*_s-2}u,\ \ \hbox{in}\ \ \mathbb{R}^N, $$ where $K(|x|)$ is a positive radial function, $N>2+2s$, $0<s<1$, and…

This paper is concerned with existence of normalized ground state solutions for the mass supercritical fractional nonlinear Schr\"{o}dinger equation involving a critical growth in the fractional Sobolev sense. The compactness of…

In this work we analyze a class of nonlinear fractional elliptic systems involving Hardy--type potentials and coupled by critical Hardy-Sobolev--type nonlinearities in $\mathbb{R}^N$. Due to the lack of compactness at the critical exponent…

We study the existence and the profile of sign-changing solutions to the slightly subcritical problem $$ -\De u=|u|^{2^*-2-\eps}u \hbox{in} \cB, \quad u=0 \hbox{on}\partial \cB, $$ where $\cB$ is the unit ball in $\rr^N$, $N\geq 3$,…

We prove existence and multiplicity results for the fractional Schroedinger--Poisson--Slater equation $(-\Delta)^s u + (I_\alpha * u^2)u = f(|x|,u)$ in $\mathbb{R}^N$, where $0<s<1$ and $\alpha \in (1,N)$. We seek solutions in a fractional…

In this paper we study dynamical properties of blowup solutions to the focusing mass-critical nonlinear fractional Schr\"odinger equation. We establish a profile decomposition and a compactness lemma related to the equation. As a result, we…