Related papers: On a variational method for solving a class of $p$…

In this work we are concerned with the following class of equations \[ -\Delta_p u -\lambda h(x)|u|^{p-2}u=f(x)|u|^{\gamma-2}u, \quad \mbox{in } \mathbb{R}^N, \] involving indefinite weight functions. The existence of solution may depend on…

In this work, we study the following Kirchhoff equation $$\begin{cases}-\left(\varepsilon^2 a+\varepsilon b\int_{\mathbb R^3}|\nabla u|^2\right)\Delta u +u =Q(x)u^{q-1},\quad u>0,\quad x\in {\mathbb{R}^{3}},\\u\to 0,\quad \text{as}\ |x|\to…

We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of…

We discuss the Kirchhoff-type $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the mountain pass theorem and the genus properties in critical point theory, we get some new results on…

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

Using the method of Nehari manifold, we prove the existence of at least two distinct weak solutions to elliptic equation of four order with singulatities and with critical Sobolev growth.

In this note, we establish a multiplicity theorem for a nonlocal discrete problem of the type $$\cases{-\left(a\sum_{m=1}^{n+1}|x_m-x_{m-1}|^2+b\right)(x_{k+1}-2x_k+x_{k-1})=h_k(x_k)\hskip 10pt k=1,...,n, \cr & \cr x_0=x_{n+1}=0\cr}$$…

We consider the following Kirchhoff - Choquard equation \[ -M(\|\na u\|_{L^2}^{2})\De u = \la f(x)|u|^{q-2}u+ \left(\int_{\Om}\frac{|u(y)|^{2^*_{\mu}}}{|x-y|^{\mu}}dy\right)|u|^{2^*_{\mu}-2}u \; \text{in}\; \Om,\quad u = 0 \; \text{ on }…

In this article we study the existence of solutions to the system \begin{equation*}\left\{ \begin{array}{ll} -\left(a+b\int_{\Omega}|\nabla u|^{2}\right)\Delta u +\phi u= f(x, u) &\text{in }\Omega \hbox{} -\Delta \phi= u^{2} &\text{in…

In this paper we consider the following class of elliptic problems $$- \Delta_A u + u = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u ,\,\, x\in \mathbb{R}^N$$ where $1<q<2<p<2^*-1= \frac{N+2}{N-2}$, $a_{\lambda}(x)$ is a sign-changing…

We propose existence and multiplicity results for the system of Schr\"odinger equations with sign-changing nonlinearities in bounded domains or in the whole space $\mathbb{R}^N$. In the bounded domain we utilize the classical approach via…

In this paper we study the existence of a least energy sign-changing solution to a nonlocal elliptic PDE involving singularity by using the Nehari manifold method, the constraint variational method and Brouwer degree theory.

In this paper, we study certain critical Schr\"{o}dinger-Kirchhoff type systems involving the fractional $p$-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari…

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,\\…

Inhomogeneous Kirchhoff type equations with indefinite data are considered. Some necessary and sufficient conditions for the existence of positive solutions of the problem under consideration are presented.

In this paper we establish the existence of at least two weak solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearity \begin{equation*} \left\{\begin{split}…

In this article we study modified Kirchhoff-Schr\"odinger equations involving critical Stein-Weiss type nonlinearity and $p$-Laplacian

We consider a nonlocal differential equation of Kirchhoff type with a convolution coefficient involving variable growth. The novelty of our work lies in allowing a variable exponent in the nonlocal term. By relating the variable growth…

In this present paper, we investigate a new class of singular double phase $p$-Laplacian equation problems with a $\psi$-Hilfer fractional operator combined from a parametric term. Motivated by the fibering method using the Nehari manifold,…

In this paper we prove the multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents. The main tool used is in the proof are the direct methods, Ekeland's variational principle and some…