Related papers: Radial solutions for a quasilinear elliptic system…

We consider the existence of \emph{normalized} solutions in $H^1(\R^N) \times H^1(\R^N)$ for systems of nonlinear Schr\"odinger equations which appear in models for binary mixtures of ultracold quantum gases. Making a solitary wave ansatz…

We provide new results on the existence, non-existence and multiplicity of non-negative radial solutions for semilinear elliptic systems with Neumann boundary conditions on an annulus. Our approach is topological and relies on the classical…

In this paper we establish a new existence result for the quasilinear elliptic problem \[ -{\rm div}(A(x,u)|\nabla u|^{p-2}\nabla u) +\frac1p A_t(x,u)|\nabla u|^p + V(x)|u|^{p-2} u = g(x,u)\quad\mbox{ in } \mathbb{R}^N, \] with $N\ge 2$,…

In this paper, we are concerned with the uniqueness and the non-degeneracy of positive radial solutions for a class of semilinear elliptic equations. Using detailed ODE analysis, we extend previous results to cases where nonlinear terms may…

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…

In this paper, we consider the following nonlinear Schr\"odinger system in $R^3$: \begin{align*} -\Delta u_j +P_j(x) u=\mu_j u_j^3+\sum\limits_{i=1,i\neq j}^N\beta_{ij}u_i^2u_j, \end{align*} where $N\geq3$, $P_j$ are nonnegative radial…

We investigate the existence of solutions to the fractional nonlinear Schr\"{o}dinger equation $(-\Delta)^s u = f(u)$ with prescribed $L^2$-norm $\int_{\mathbb{R}^N} |u|^2 \, dx =m$ in the Sobolev space $H^s(\mathbb{R}^N)$. Under fairly…

Assuming $B_{R}$ is a ball in $\mathbb R^{N}$, we analyze the positive solutions of the problem \[ \begin{cases} -\Delta u+u= |u|^{p-2}u, &\text{ in } B_{R},\newline \partial_{\nu}u=0,&\text{ on } \partial B_{R}, \end{cases} \] that branch…

We study the following quasilinear elliptic system for all $i=1,\cdots,m$ \begin{equation*} \label{} -div(\Phi'(|\nabla u_i|^2) \nabla u_i) = H_i(u) \quad \text{in} \ \ \mathbb{R}^n \end{equation*} where $u=(u_i)_{i=1}^m: \mathbb R^n\to…

We investigate the existence and nonexistence of positive solutions for the quasilinear elliptic inequality $L_\mathcal{A} u= -{\rm div}[\mathcal{A}(x, u, \nabla u)]\geq (I_\alpha\ast u^p)u^q$ in $\Omega$, where $\Omega\subset \mathbb{R}^N,…

This paper deals with the following fractional Schr$ \ddot{\textrm{o}}$dinger equations with Choquard-type nonlinearities \begin{equation*} \left\{\begin{array}{r@{\ \ }c@{\ \ }ll} (-\Delta)^{\frac{\alpha}{2}}u + u - C_{n,-\beta}…

The existence of radially symmetric solutions is discussed for a Lane-Emden type system. This answer a question posed by da Silva and do O (2024). We also comment on the inhomogeneous version of the same system and discuss some open…

In this paper we investigate the existence of positive solution for a class of quasilinear problem on an Orlicz-Sobolev space that can be nonreflexive $$- \Delta_{\Phi} u +V(x)\phi(|u|)u= K(x)f(u)\mbox{ in } \mathbb{R}^{N}$$ where $N\geq2$,…

In this paper, we deal with the following quasilinear elliptic system involving gradient terms in the form: \begin{center} $\begin{cases} \Delta_p u= v^m| \nabla u |^\alpha& \text{in}\quad \Omega\\ \Delta_p v= v^\beta| \nabla u |^q &…

We consider the stationary semilinear Schr\"odinger equation $-\Delta u + a(x) u = f(x,u)$, $u\in H^1(\R^N)$, where $a$ and $f$ are continuous functions converging to some limits $a_\infty>0$ and $f_\infty=f_\infty(u)$ as $|x|\to\infty$. In…

In this paper we consider the following quasilinear Schr\"odinger-Poisson system in a bounded domain in $\mathbb{R}^{2}$: $$ \left\{ \begin{array}[c]{ll} - \Delta u +\phi u = f(u) &\ \mbox{in } \Omega, -\Delta \phi - \varepsilon^{4}\Delta_4…

We consider the Schr\"odinger--Poisson system on the complete, simply-connected Riemannian manifolds of constant sectional curvature. We obtain closed-form stationary spherically-symmetric solutions for the homogeneous equations for certain…

We prove new results on the existence of positive radial solutions of the elliptic equation $-\Delta u= \lambda h(|x|,u)$ in an annular domain in $\mathbb{R}^{N}, N\geq 2$. Existence of positive radial solutions are determined under the…

The aim of this paper is investigating the existence of weak bounded solutions of the gradient-type quasilinear elliptic system $$(P)\qquad \left\{ \begin{array}{ll} - {\rm div} ( a_i(x, u_i, \nabla u_i) ) + A_{i, t} (x, u_i, \nabla u_i) =…

We consider the focussing energy-critical inhomogeneous nonlinear Schr\"odinger equation: $$ iu_t + \Delta u + g|u|^2u = 0, u(0)= \varphi \in \dot{H}^1,\;\; 0 \le g_i \le |x|g \le g_s.$$ On the road map of Kenig-Merle \cite{km} we show the…