相关论文: Sign changing solutions of the Brezis-Nirenberg pr…

We study the a priori estimates,existence/nonexistence of radial sign changing solution, and the Palais-Smale characterisation of the problem $-\De_{\Bn}u - \la u = |u|^{p-1}u, u\in H^1(\Bn)$ in the hyperbolic space $\Bn$ where…

We consider the classical Brezis-Nirenberg problem in the unit ball of $\mathbb{R}^N$, $N\geq 3$ and analyze the asymptotic behavior of nodal radial solutions in the low dimensions $N=3,4,5,6$ as the parameter converges to some limit value…

This article investigates the multiplicity of solutions to the Brezis-Nirenberg problem on smooth bounded domains in the hyperbolic space $\mathbb{B}^N$ for $N \ge 4$. Specifically, we study the critical semilinear equation…

The main purpose of this paper is to establish the existence, nonexistence and symmetry of nontrivial solutions to the higher order Brezis-Nirenberg problems associated with the GJMS operators $P_k$ on bounded domains in the hyperbolic…

We consider semilinear elliptic problems on two-dimensional hyperbolic space involving critical growth. We first establish the Palais-Smale(P-S) condition and using (P-S) condition we obtain existence of solutions. In addition, we also…

In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Firstly, we get periodic solutions using suitable constraints,…

In this paper, we consider the existence and non-existence of non-trivial solution to a Brezis-Nirenberg type problem with singular weights. First, we obtain a compact imbedding theorem which is an extension of the classical…

We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…

We consider the log-perturbed Br\'ezis-Nirenberg problem on the hyperbolic space \begin{align*} \Delta_{\mathbb{B}^N}u+\lambda u +|u|^{p-1}u+\theta u \ln u^2 =0, \ \ \ \ u \in H^1(\mathbb{B}^N), \ u > 0 \ \mbox{in} \ \mathbb{B}^N,…

We consider the Brezis-Nirenberg problem: \begin{equation*} \begin{cases} -\Delta u = \lambda u + |u|^{2^* -2}u & \hbox{in}\ \Omega\\ u=0 & \hbox{on}\ \partial \Omega, \end{cases} \end{equation*} where $\Omega$ is a smooth bounded domain in…

In this paper we consider a mean field problem on a compact surface with conical singularities. This problem appears in the Gaussian curvature prescription problem in Geometry, and also in the Electroweak Theory and in the abelian…

In this work, we develop a study involving some nonlinear partial differential equations on spheres and hemispheres, with the zero Neumann boundary condition, which are so-called Brezis-Nirenberg type problems, and we give conditions on…

In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a complete resolution to the first one--Open Problem 1.1--in…

We study the asymptotic behavior, as $\lambda \rightarrow 0$, of least energy radial sign-changing solutions $u_\lambda$, of the Brezis-Nirenberg problem \begin{equation*} \begin{cases} -\Delta u = \lambda u + |u|^{2^* -2}u & \hbox{in}\…

In this paper we study the asymptotic and qualitative properties of least energy radial sign-changing solutions of the fractional Brezis--Nirenberg problem ruled by the s-laplacian, in a ball of $\mathbb{R}^n$, when $s \in (0,1)$ and $n >…

In this paper, we investigate the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary. The existence result is assured under some geometric conditions.

In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems…

In this article, we study the following Hardy-Sobolev-Maz'ya type equation: \begin{equation} -\Delta u - \mu \frac{u}{|z|^2} = \frac{|u|^{q-2}u}{|z|^t}, \quad u \in D^{1,2} (\mathbb{R}^n), \end{equation} where $x = (y,z) \in \mathbb{R}^h…

We consider a certain ultrahyperbolic equation in a Euclidean space being a generalization of Klein-Gordon-Fock equation. The behavior of solutions at points tending to infinity along timelike directions is studied. We examine the issue of…

This paper is devoted to study a class of integral type Brezis-Nirenbreg problem on the Heisenberg group. It is a class of new nonlinear integral equations on the bounded domains of Heisenberg group and related to the CR Yamabe problems on…