Related papers: Three solutions for a new Kirchhoff-type problem
In this paper, we consider the multiplicity of solutions for a class of Kirchhoff type problems with sub-linear and critical terms on an unbounded domain. With the aid of Ekeland's variational principle and the concentration compactness…
This paper is dedicated to studying the existence of nontrivial positive solutions for a Kirchhoff-type problem with sign change nonlinearities and a singular term, Using the Nehari manifold and EkelandS variational principle we prove that…
Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of…
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…
The purpose of this paper is to study the indefinite Kirchhoff type problem: \begin{equation*} \left\{ \begin{array}{ll} M\left( \int_{\mathbb{R}^{N}}(|\nabla u|^{2}+u^{2})dx\right) \left[ -\Delta u+u\right] =f(x,u) & \text{in…
Consider the following Kirchhoff type problem $$ \left\{\aligned -\bigg(a+b\int_{\mathbb{B}_R}|\nabla u|^2dx\bigg)\Delta u&= \lambda u^{q-1} + \mu u^{p-1}, &\quad \text{in}\mathbb{B}_R, \\ u&>0,&\quad\text{in}\mathbb{B}_R,\\…
In this paper we are concerned with some $p$-Kirchhoff type problems involving sign-changing weight functions. We prove the existence of multiple positive solutions of the problem via the Nehari manifold approach.
In this paper we establish the existence of mountain pass and negative energy weak solutions for a Kirchhoff-Schr\"odinger type problem in $\mathbb R^4$ involving a critical nonlinearity and a suitable small perturbation. The arisen…
In this paper, by using variational methods we study the existence of positive solutions for the following Kirchhoff type problem: $$ \left\{ \begin{array}{ll} -\left(a+b\mathlarger{\int}_{\Omega}|\nabla u|^{2}dx\right)\Delta u+V(x)u=u^{5},…
By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a $(p,q)$-Kirchhoff elliptic system with the Dirichlet boundary conditions and…
In this paper, a critical fourth-order Kirchhoff type elliptic equation with a subcritical perturbation is studied. The main feature of this problem is that it involves both a nonlocal coefficient and a critical term, which bring essential…
In this paper, we study the existence of three solutions for a Kirchhoff equation involving the nonlocal fractional p-Laplacian considering Sobolev and Hardy nonlinearities at subcritical and critical growths. The proof is based on Mountain…
In this paper, a critical Kirchhoff equation with a logarithmic type subcritical term is considered in a bounded domain in $\mathbb{R}^4$. We view this problem as a critical elliptic equation with a nonlocal perturbation, and investigate…
This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…
In this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left\{ \begin{aligned} -(1+b \int_{\mathbb{R}^3}|\nabla u|^2)\Delta u= k(x)\frac{|u|^2 u}{|x|} +\lambda…
In the present paper, we are interested in investigating the existence of positive solutions of a new class of fractional Kirchhoff via the sub and supersolutions technique. For this, we first need to investigate two results through lemmas.
We study the non-existence, existence and multiplicity of positive solutions to the following nonlinear Kirchhoff equation:% \begin{equation*} \left\{ \begin{array}{l} -M\left( \int_{\mathbb{R}^{3}}\left\vert \nabla u\right\vert…
In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter.…
In this note, we deal with a problem of the type $$\cases {-h\left ( \int_{\Omega}|\nabla u(x)|^2dx\right ) \Delta u=f(u) & in $\Omega$\cr & \cr u_{|\partial\Omega}=0\ .\cr}$$ As an application of a new general multiplicity result, we…
In this paper, we are going to study the existence of solution for the following Kirchhoff problem $$ \left\{ \begin{array}{l} M\biggl(\displaystyle\int_{\mathbb{R}^{3}}|\nabla u|^{2} dx +\displaystyle\int_{\mathbb{R}^{3}} \lambda…