Related papers: Normalized solutions to a class of $(2,q)$-Laplaci…
In this paper, we study normalized ground states for the following critical fractional NLS equation with prescribed mass: \begin{equation*} \begin{cases} (-\Delta)^{s}u=\lambda u +\mu|u|^{q-2}u+|u|^{2_{s}^{\ast}-2}u,&x\in\mathbb{R}^{N},…
In this paper, we study normalized ground state solutions for the following nonautonomous Choquard equation: $$-\Delta u-\lambda u=\left(\frac{1}{|x|^{\mu}}\ast A|u|^{p}\right)A|u|^{p-2}u,\quad \int_{\mathbb{R}^{N}}|u|^{2}dx=c,\quad u\in…
This paper focuses on the existence and multiplicity of normalized solutions for the coupled Schrodinger system with Sobolev critical coupling term. We present several existence and multiplicity results under some explicit conditions.…
We study the problem \begin{eqnarray*} (-\Delta)^s u &=& u^p - u^q \quad\text{in }\quad \mathbb{R}^N, u &\in& \dot{H}^s(\mathbb{R}^N)\cap L^{q+1}(\mathbb{R}^N), u&>0& \quad\text{in}\quad\mathbb{R}^N, \end{eqnarray*} where $s\in(0,1)$ is a…
We obtain nontrivial solutions of a critical $(p,q)$-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a…
We study the normalized solutions to the following Choquard equation \begin{equation*} \aligned &-\Delta u + \lambda u =\mu g(u) + \gamma (I_\alpha * |u|^{\frac{N+\alpha}{N}})|u|^{\frac{N+\alpha}{N}-2}u & \text{in\ \ } \mathbb{R}^N…
In this paper, we consider the existence of normalized solutions for the following $p$-Laplacian equation \begin{equation*} \left\{\begin{array}{ll} -\Delta_{p}u-V(x)\lvert u\rvert^{p-2}u+\lambda\lvert u\rvert^{p-2}u=\lvert…
In this paper, we study the existence of multiple normalized solutions to the following dipolar Gross-Pitaveskii equation with a mass subcritical perturbation \begin{align*} \left\{ \begin{array}{lll} -\frac{1}{2}\Delta u+\mu…
In this paper, we study the existence of normalized solutions to the following Kirchhoff equation with a perturbation: $$ \left\{ \begin{aligned} &-\left(a+b\int _{\mathbb{R}^{N}}\left | \nabla u \right|^{2} dx\right)\Delta u+\lambda…
In this paper, we consider the existence of positive solutions with prescribed $L^2$-norm for the following nonlinear Schr\"{o}dinger equation involving potential and Sobolev critical exponent \begin{equation*} \begin{cases} -\Delta…
We investigate normalized groundstates for mixed $(p,2)$-Laplacian equations \begin{align*} \begin{cases} -\Delta_p u-\Delta u+\lambda u=f(u) & \text{in } \mathbb{R}^2, \displaystyle \int_{\mathbb{R}^2}|u|^2\,\mathrm{d}x=m, u\in…
We consider the existence of normalized solutions to nonlinear Schr\"odinger equations on noncompact metric graphs in the $L^2$ supercritical regime. For sufficiently small prescribed mass ($L^2$ norm), we prove existence of positive…
We look for normalized solutions to the nonlinear Schr\"{o}dinger equation with mixed fractional Laplacians and combined nonlinearities $$ \left\{\begin{array}{ll} (-\Delta)^{s_{1}} u+(-\Delta)^{s_{2}} u=\lambda u+\mu |u|^{q-2}u+|u|^{p-2}u…
We consider the critical Choquard system with both linear and nonlinear couplings $-\Delta v_1 + \mu_1 v_1 = ( I_\omega * |v_1|^{2_\omega^*} ) |v_1|^{2_\omega^* -2} v_1 + \theta p( I_\omega * |v_2|^q)|v_1|^{p-2} v_1 + \varepsilon v_2, \quad…
For $p>2$, we consider the quasilinear equation $-\Delta_p u+|u|^{p-2}u=g(u)$ in the unit ball $B$ of $\mathbb R^N$, with homogeneous Neumann boundary conditions. The assumptions on $g$ are very mild and allow the nonlinearity to be…
This paper studies the multiplicity of normalized solutions to the Schr\"{o}dinger equation with mixed nonlinearities \begin{equation*} \begin{cases} -\Delta u=\lambda u+h(\epsilon x)|u|^{q-2}u+\eta |u|^{p-2}u,\quad x\in \mathbb{R}^N, \\…
We investigate normalized solutions for a class of nonlinear Schr\"{o}dinger (NLS) equations with potential $V$ and inhomogeneous nonlinearity $g(|u|)u=|u|^{q-2}u+\beta |u|^{p-2}u$ on a bounded domain $\Omega$. Firstly, when…
In the present work we briefly explain how to adapt techniques already used in fractional and $p$-fractional Laplacian cases to obtain the existence of a nontrivial solution at the mountain pass level and a nontrivial ground state solution,…
In this article, we study the existence and multiplicity of solutions of the following $(p,q)$-Laplace equation with singular nonlinearity: \begin{equation*} \left\{\begin{array}{rllll} -\Delta_{p}u-\ba\Delta_{q}u & = \la u^{-\de}+ u^{r-1},…
In this paper, we study the existence of normalized solutions to the following nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{ \begin{aligned} &-\Delta u=f(u)+ \lambda u\quad \mbox{in}\ \mathbb{R}^{N},\\ &u\in…