相关论文: Choquard equations with critical exponential nonli…

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}…

In this paper, an autonomous Choquard equation with the upper critical exponent is considered. By using the Poho\v{z}aev constraint method, the subcritical approximation method and the compactness lemma of Strauss, a groundstate solution in…

We consider the two-dimensional eigenvalue problem for the Laplacian with the Neumann boundary condition involving the critical Hardy potential. We prove the existence of the second eigenfunction and study its asymptotic behavior around the…

In this paper we are interested in the following nonlinear Choquard equation $$ -\Delta u+(\lambda V(x)-\beta)u =\big(|x|^{-\mu}\ast |u|^{2_{\mu}^{\ast}}\big)|u|^{2_{\mu}^{\ast}-2}u\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N, $$…

We propose an existence result for the semirelativistic Choquard equation with a local nonlinearity in $\mathbb{R}^N$ \begin{equation*} \sqrt{\strut -\Delta + m^2} u - mu + V(x)u = \left( \int_{\mathbb{R}^N}…

In this article, we study the following problem $$-{\rm div} (\omega(x)|\nabla u|^{N-2} \nabla u) = \lambda\ f(x,u) \quad\mbox{ in }\quad B, \quad u=0 \quad\mbox{ on } \quad\partial B,$$ where $B$ is the unit ball of $\mathbb{R^{N}}$,…

In the present work we investigate the existence and multiplicity of nontrivial solutions for the Choquard Logarithmic equation $(-\Delta)^{\frac{1}{2}} u + au + \lambda (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ in } \mathbb{R}$, for $ a>0…

We consider non-gauge-invariant cubic nonlinear Schr\"odinger equations in one space dimension. We show that initial data of size $\varepsilon$ in a weighted Sobolev space lead to solutions with sharp $L_x^\infty$ decay up to time…

We study the logarithmic Schr\"odinger equation with finite range potential on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we associate and construct a global Gibbs measure and show that it satisfies a logarithmic…

In the present work, we consider a fractional p-Kirchhoff equation in the entire space R^N featuring doubly nonlinearities, involving a generalized nonlocal Choquard subcritical term together with a local critical Sobolev term; the problem…

We study fourth-order quasilinear elliptic problems that involve the p-biharmonic operator and Navier boundary conditions. The nonlinear term grows at the critical Sobolev rate. Starting from a Hamiltonian system of two second-order…

Using a variational method we prove the existence of nodal solutions to prescribed scalar Q- curvature type equations on compact Riemannian manifolds with boundary; these equations are fourth-order elliptic equations with critical Sobolev…

We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…

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…

We study existence results for a problem with criticical Sobolev exponent and with a positive weight.

For the Choquard equation, which is a nonlocal nonlinear Schr\"odinger type equation, $ -\Delta u+V_{\mu,\nu} u=(I_\alpha\ast |u|^{\frac{N+\alpha}{N}}){|u|}^{\frac{\alpha}{N}-1}u$, in $\mathbb{R}^N$ where $N\ge 3$, $V_{\mu, \nu} :…

In this paper, we consider the existence of positive solutions to the following slightly supercritical Choquard equation \begin{equation*} \begin{cases} -\Delta…

We consider semilinear elliptic problems of the form \[ -\Delta u + \lambda u = f(x,u), \quad u\in H^1_0(A), \] where $A\subset\mathbb{R}^N$, $N\geq3$, is either a bounded or unbounded annulus, and $\lambda \geq0$. We study a broad class of…

We establish some existence results for a class of critical elliptic problems with singular exponential nonlinearities. We do not assume any global sign conditions on the nonlinearity, which makes our results new even in the nonsingular…

We are interested in finding prescribed $L^2$-norm solutions to inhomogeneous nonlinear Schr\"{o}dinger (INLS) equations. For $N\ge 3$ we treat the equation with combined Hardy-Sobolev power-type nonlinearities $$ -\Delta u+\lambda…