相关论文: Normalized solutions for the NLS equation with pot…

We consider the existence and multiplicity of positive solutions for the following critical problem with logarithmic term: \begin{equation*}\label{eq11}\left\{ \begin{array}{ll} -\Delta u={\mu\left|u\right|}^{{2}^{\ast }-2}u+\nu…

In this paper we establish the existence of mountain pass and negative energy weak solutions for a Kirchhoff-Schr\"odinger type problem in $\mathbb R^4$ involving a critical nonlinearity and a suitable small perturbation. The arisen…

In this work, we establish the multiplicity of positive solutions for the following critical fractional Choquard equation with a perturbation on the star-shaped bounded domain $$ \left\{ \begin{array}{lr} (-\Delta)^s u = \lambda u…

We consider the existence of solutions for nonlinear Schr\"odinger equations on noncompact metric graphs with localized nonlinearities. In an $L^2$-supercritical regime, we establish the existence of infinitely many solutions for any…

This paper concerns the existence of normalized solutions to a class of $(2,q)$-Laplacian equations in all the possible cases according to the value of $p$ with respect to the critical exponent $2(1+2/N)$. In the $L^2$-subcritical case, we…

We study normalised solutions for a Choquard equation in the plane with polynomial Riesz kernel and exponential nonlinearities, which are critical in the sense of Trudinger-Moser. For all prescribed values of the mass, we prove existence of…

We are concerned with the normalized $\ell$-peak solutions to the nonlinear Schr\"{o}dinger equation \[ -\varepsilon^2\Delta v+V(x)v=f(v)+\lambda v,\quad \int_{\mathbb{R}^N}v^2 =\alpha \varepsilon^N. \] Here $\lambda \in \mathbb{R}$ will…

We provide an existence result for a Schr\"odinger-Poisson system in gradient form, set in the whole plane, in the case of zero mass. Since the setting is limiting for the Sobolev embedding, we admit nonlinearities with subcritical or…

We investigate normalized solutions with prescribed $L^2$-norm for the upper critical fractional Choquard equation \[(-\Delta)^s u+V(\varepsilon x)u=\lambda…

A nonlinear Schr\"odinger equation with external potential $-(t+b)^{-1}$ is considered and its explicit solutions are constructed.

We study the existence of solutions $(\underline u,\lambda_{\underline u})\in H^1(\mathbb{R}^N; \mathbb{R}) \times \mathbb{R}$ to \[ -\Delta u + \lambda u = f(u) \quad \text{in } \mathbb{R}^N \] with $N \ge 3$ and prescribed $L^2$ norm, and…

We consider the mass-subcritical NLS in dimensions $d\geq 3$ with radial initial data. In the defocusing case, we prove that any solution that remains bounded in the critical Sobolev space throughout its lifespan must be global and scatter.…

We study the existence of positive solutions on $\R^{N+1}$ to semilinear elliptic equation $-\Delta u+u=f(u)$ where $N\geq 1$ and $f$ is modeled on the power case $f(u)=|u|^{p-1}u$. Denoting with $c$ the mountain pass level of $\f(u)=\tfrac…

In this paper, we study normalized solutions to the Chern-Simons-Schr\"odinger system, which is a gauge-covariant nonlinear Sch\"oridnger system with a long-range electromagnetic field, arising in nonrelativistic quantum mechanics theory.…

In this paper, we consider the existence, multiplicity and nonexistence of solutions for the following equation \begin{equation*} \begin{cases} \begin{aligned} &-\Delta u+\omega u=\mu u^{p-1}+u^{q-1},~ u>0 \quad &&\text { in } \Omega, \\…

In this paper we study the multiplicity of normalized solutions to the following nonlinear Schr\"{o}dinger equation with critical growth \begin{align*} \left\{ \begin{aligned} &-\Delta u=\lambda u+\mu |u|^{q-2}u+f(u), \quad \quad \hbox{in…

This paper presents a new approach for addressing the singularly perturbed nonlinear Schr\"odinger (NLS) equation: \begin{equation} -\varepsilon^2\Delta v + V(x) v =f(v),\ v>0,\ \lim_{|x|\to \infty} v(x)=0, \end{equation} where $V$…

We consider the long time well-posedness of the Cauchy problem with large Sobolev data for a class of nonlinear Schr\"odinger equations (NLS) on $\mathbb{R}^2$ with power nonlinearities of arbitrary odd degree. Specifically, the method in…

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…

This paper is concerned with the following logarithmic Schr\"{o}dinger system: $$\left\{\begin{align} \ &\ -\Delta u_1+\omega_1u_1=\mu_1 u_1\log u_1^2+\frac{2p}{p+q}|u_2|^{q}|u_1|^{p-2}u_1,\\ \ &\ -\Delta u_2+\omega_2u_2=\mu_2 u_2\log…