相关论文: Normalized Solutions for the $(2,q)$-Laplacian Ope…

In this work we deal with the class of nonlinear (p,q)-Laplacian system. Non-existence results of positive weak solutions for this system are established.

We study the following nonlinear Schr\"odinger equation and we look for normalized solutions $(\mu,u)\in {\bf R}\times H^1({\bf R}^N)$ for a given $m>0$ and $N\geq 2$ \[ -\Delta u + \mu u = g(u)\quad \text{in}\ {\bf R}^N, \qquad…

We analyze the existence and multiplicity of positive solutions to a nonlocal elliptic problem involving the spectral fractional Laplace operator endowed with homogeneous mixed Dirichlet-Neumann boundary conditions and weighted critical…

A homogeneous Dirichlet problem with $(p,q)$-Laplace differential operator and reaction given by a parametric $p$-convex term plus a $q$-concave one is investigated. A bifurcation-type result, describing changes in the set of positive…

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…

This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-\Delta)^s u+V(x) u=\lambda u+f(x)\left(I_\alpha *\left(f|u|^q\right)\right)|u|^{q-2} u+g(x)\left(I_\alpha…

This paper is devoted to studying the existence of normalized solutions for the following quasilinear Schr\"odinger equation \begin{equation*} \begin{aligned} -\Delta u-u\Delta u^2 +\lambda u=|u|^{p-2}u \quad\mathrm{in}\ \mathbb{R}^{N},…

In this paper, we are interested in studying the existence or non-existence of solutions for a class of elliptic problems involving the $N$-Laplacian operator in the whole space. The nonlinearity considered involves critical Trudinger-Moser…

We are concerned with the following system of two coupled time-independent Gross-Pitaevskii equations $$ \begin{cases} -\Delta u+\lambda_1 u=\mu_1|u|^{p-2}u+\nu\alpha |u|^{\alpha-2}|v|^{\beta}u ~\hbox{in}~ \R^N,\\ -\Delta v+\lambda_2…

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish…

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…

We study normalized solutions for the nonlinear Schrodinger (NLS) equation with potential and Sobolev critical nonlinearity. By establishing suitable assumptions on the potential, together with new techniques, we find a mountain-pass type…

In this paper, we consider the critical Choquard system with prescribed mass \begin{equation*} \begin{aligned} \left\{ \begin{array}{lll} -\Delta u+\lambda_1u=(I_\mu\ast |u|^{2^*_\mu})|u|^{2^*_\mu-2}u+\nu p(I_\mu\ast |v|^q)|u|^{p-2}u\ &…

We consider a $(p,2)$-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a $p$-Laplacian and a Laplacian with $p>2$. The reaction term is $(p-1)$-linear but exhibits asymmetric behaviour at $\pm\infty$ and…

We consider Dirichlet elliptic equations driven by the sum of a $p$-Laplacian $(2<p)$ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both $\pm\infty$ and at zero. We prove an existence theorem…

In this paper, we study the existence of normalized solutions for the nonautonomous Schr\"{o}dinger-Poisson equations \begin{equation}\nonumber -\Delta u+\lambda u +\left(\vert x \vert ^{-1} * \vert u \vert ^{2} \right)…

We analyze a non-linear elliptic boundary value problem, that involves $(p, q)$ Laplace operator, for the existence of its positive solution in an arbitrary smooth bounded domain. The non-linearity here is driven by a continuous function in…

In this paper, we focus on (no)existence and asymptotic behavior of solutions for the double critical Maxwell equation involving with the Hardy, Hardy-Sobolev, Sobolev critical exponents. The existence and noexistence of solutions…

A Dirichlet problem driven by the $(p,q)$-Laplace operator and an asymmetric concave reaction with positive parameter is investigated. Four nontrivial smooth solutions (two positive, one negative, and the remaining nodal) are obtained once…

In this paper, we are concerned with the following fractional $N/s$-Laplacian Choquard equation \begin{align*} \begin{cases} (-\Delta)^s_{N/s}u=\lambda |u|^{\frac{N}{s}-2}u +(I_\mu*F(u))f(u),\ \ \mbox{in}\ \mathbb{R}^N,…