Related papers: Entire solutions to a quasilinear purely critical …

The main purpose of this paper is to establish the existence of positive solutions to a class of quasilinear elliptic equations involving the (p-q)-Laplacian operator. We consider a nonlinearity that can be subcritical at infinity and…

In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $-\Delta_p u = |u|^{p^*-2}u + \lambda f(x,u)$ in a smooth bounded domain $\Omega$ of $\R^N$ with homogeneous Dirichlet…

We focus on the study of $p$-Laplacian Dirichlet problem containing the left and right fractional derivative operators. By using the genus properties in critical point theory, we establish some new criteria to guarantee the existence of…

In this paper we develop a new theory for the existence, localization and multiplicity of positive solutions for a class of non-variational,quasilinear, elliptic systems. In order to do this, we provide a fairly general abstract framework…

This paper deals with existence of solutions to the following fractional $p$-Laplacian system of equations \begin{equation*} %\tag{$\mathcal P$}\label{MAT1} \begin{cases} (-\Delta_p)^s u =|u|^{p^*_s-2}u+…

We prove the existence of a positive solution to a semipositone $N$-Laplacian problem with a critical Trudinger-Moser nonlinearity. The proof is based on obtaining uniform $C^{1,\alpha}$ a priori estimates via a compactness argument. Our…

We show the existence of nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. A nonexistence result is also given.

In the present paper, we are concerned with entire radially symmetric solutions for a quasilinear system with phi{i}-Laplacian operator.

In this paper we will prove the existence of three nontrivial weak solutions of the following problem involving a nonlinear integro-differential operator and a term with critical exponent. \begin{align*} \begin{split} -\mathscr{L}_\Phi u &…

In this paper, we consider the nonlocal elliptic problems in $\mathbb{R}^{N}$, which involve finite many critical exponents. By using endpoint refined Hardy--Sobolev inequality, fractional Coulomb--Sobolev space and variational method, we…

We investigate the existence of nonnegative solutions for a nonlinear problem involving the fractional p-Laplacian operator. The problem is set on a unbounded domain, and compactness issues have to be handled.

In this paper, we deal with a singular quasilinear critical elliptic equation of Lichnerowicz type involving the p-Laplacian operator. With the help of the subcritical approach from variational method, we obtain the non-existence,…

In this article a nonlocal elliptic problem involving $p$-Laplacian on unbounded domain is considered. Using variational methods and under suitable conditions, the existence of a sequence of radially symmetric weak solutions, in two…

In this paper, we show some results about the existence and the uniqueness of the positive solution for a $p$-Laplacian fractional differential equations with fractional derivative boundary condition. Our results are based on…

We obtain nontrivial solutions of a $(N,q)$-Laplacian problem with a critical Trudinger-Moser nonlinearity in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical…

The paper deals with the existence of non-radial solutions for an $N$-coupled nonlinear elliptic system. In the repulsive regime with some structure conditions on the coupling and for each symmetric subspace of rotation symmetry, we prove…

The main purpose of this paper is to exhibit a simple variational setting for finding fully nontrivial solutions to the weakly coupled elliptic system (1.1). We show that such solutions correspond to critical points of a…

We study the existence of fully nontrivial solutions to the system $$-\Delta u_i+ \lambda_iu_i = \sum\limits_{j=1}^\ell \beta_{ij}|u_j|^p|u_i|^{p-2}u_i\ \hbox{in}\ \Omega, \qquad i=1,\ldots,\ell,$$ in a bounded or unbounded domain $\Omega$…

In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the $p(x)-$Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies…

The existence of a positive entire weak solution to a singular quasi-linear elliptic system with convection terms is established, chiefly through perturbation techniques, fixed point arguments, and a priori estimates. Some regularity…