Related papers: On a Kirchhoff type problems with potential well a…

This paper gives a priori estimates for the positve solutions of Kirchhoff type equation without variational structure.

We investigate the degenerate fractional Schr\"{o}dinger-Kirchhoff-Poisson equation in $\mathbb{R}^3$ with critical nonlinearity and electromagnetic fields $\varepsilon^{2s} M([u]_{s,A}^2)(-\Delta)_{A}^su + V(x)u + \phi u = k(x)|u|^{r-2}u +…

This paper addresses the following problem. \begin{equation} \left\{ \begin{array}{lr} -{\Delta}u=\lambda I_\alpha*_\Omega u+|u|^{2^*-2}u\mbox{ in }\Omega ,\nonumber u\in H_0^1(\Omega).\nonumber \end{array} \right. \end{equation} Here,…

This paper aims to establish the existence of a weak solution for the non-local problem: \begin{equation*} \left\{\begin{array}{ll} -a\left(\int_{\Omega}\mathcal{H}(x,|\nabla u|)dx \right) \Delta_{\mathcal{H}}u &=f(x,u) \ \ \hbox{in} \ \…

We are interested in nonlinear fractional Schr\"odinger equations with singular potential of form \begin{equation*} (-\Delta)^su=\frac{\lambda}{|x|^{\alpha}}u+|u|^{p-1}u,\quad \mathbf R^n\setminus\{0\}, \end{equation*} where $s\in (0,1)$,…

The present paper deals with a parametrized Kirchhoff type problem involving a critical nonlinearity in high dimension. Existence, non existence and multiplicity of solutions are obtained under the effect of a subcritical perturbation by…

In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation \begin{equation*} -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) \end{equation*} submitted to Dirichlet boundary conditions. Under a…

In this article, we deal with the following involving $p$-biharmonic critical Choquard-Kirchhoff equation $$ \left(a+b\left(\int_{\mathbb R^N}|\Delta u|^p dx\right)^{\theta-1}\right) \Delta_{p}^{2}u = \alpha…

Let $\Omega$ be a smooth bounded domain in $\mathbb{R}^{N}$, $N\geq1$, let $K$, $M$ be two nonnegative functions and let $\alpha,\gamma>0$. We study existence and nonexistence of positive solutions for singular problems of the form $-\Delta…

We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type $p(\cdot)$-Laplacian problems involving an arbitrary growth and a sandwich-type growth $s(\cdot)\in (\inf p,\sup p)$. This setting leads to…

We investigate the existence, multiplicity and concentration of nontrivial solutions for the following fractional magnetic Kirchhoff equation with critical growth: \begin{equation*} \left(a\varepsilon^{2s}+b\varepsilon^{4s-3}…

This article deals with the study of the following Kirchhoff equation with exponential nonlinearity of Choquard type (see $(KC)$ below). We use the variational method in the light of Moser-Trudinger inequality to show the existence of weak…

In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, $$ -\Delta_p^a u-\Delta_q u =\lambda m(x) |u|^{q-2}u \quad \mbox{in} \,\, \R^N, $$ where {$N \geq 2$}, {$1<p, q<N$,…

We proceed with the investigation of the problem $(P_\lambda): $ $-\Delta u = \lambda b(x)|u|^{q-2}u +a(x)|u|^{p-2}u \ \mbox{ in } \Omega, \ \ \frac{\partial u}{\partial \mathbf{n}} = 0 \ \mbox{ on } \partial \Omega$, where $\Omega$ is a…

We study Brezis-Nirenberg type problems, governed by the double phase operator $- \mathrm{div}\left(|\nabla u|^{p-2}\, \nabla u + a(x)\, |\nabla u|^{q-2}\, \nabla u\right)$, that involve a critical nonlinearity of the form $|u|^{p^\ast -…

In this paper, we aim to tackle the questions of existence and multiplicity of solutions to a new class of $\kappa(\xi)$-Kirchhoff-type equation utilizing a variational approach. Further, we research the results from the theory of variable…

The paper deals with the equation $-\Delta u+a(x) u =|u|^{p-1}u $, $u \in H^1(\mathbb{R}^N)$, with $N\ge 2$, $p>1,\ p<{N+2\over N-2}$ if $N\ge 3$, $a\in L^{N/2}_{loc}(\mathbb{R}^N)$, $\inf a>0$, $\lim_{|x| \to \infty} a(x)= a_\infty$.…

In this paper, we are interested in the following critical Kirchhoff type elliptic equation with a logarithmic perturbation \begin{equation}\label{eq0} \begin{cases} -\left(1+b\int_{\Omega}|\nabla{u}|^2\mathrm{d}x\right) \Delta{u}=\lambda…

In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem…

We consider Kirchhoff equations with a small parameter epsilon in front of the second-order time-derivative, and a dissipative term whose coefficient may tend to 0 as t -> + infinity (weak dissipation). In this note we present some recent…