Related papers: Multiple solutions for p-Laplacian type problems w…

The paper is devoted to the existence of positive solutions of nonlinear elliptic equations with $p$-Laplacian. We provide a general topological degree that detects solutions of the problem $$ \{{array}{l} A(u)=F(u) u\in M {array}. $$ where…

We prove a result of existence of positive solutions of the Dirichlet problem for $-\Delta_p u=\mathrm{w}(x)f(u,\nabla u)$ in a bounded domain $\Omega\subset\mathbb{R}^N$, where $\Delta_p$ is the $p$-Laplacian and $\mathrm{w}$ is a weight…

We investigate the quasilinear elliptic system $-\Delta_{m} u&=u^{-p}v^{-q}$, $u>0 \quad\mbox{ in } \Omega$, $-\Delta_{m} v&=u^{r}v^{-s}$, $v>0 \quad\mbox{ in }\Omega$, $u=v=0 \quad\mbox{ on } \partial{\Omega}$, where $\Omega…

We study vector valued solutions to non-linear elliptic partial differential equations with $p$-growth. Existence of a solution is shown in case the right hand side is the divergence of a function which is only $q$ integrable, where $q$ is…

In this paper, we are concerned with the following elliptic equation $$\left\{\begin{array}{rrl}-\Delta u&=& |u|^{4/(n-2)}u/[\ln (e+|u|)]^\varepsilon\hbox{ in } \Omega,\\ u&=&0 \hbox{ on }\partial \Omega, \end{array} \right.$$ where…

In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to…

In this paper we consider the following coupled gradient-type quasilinear elliptic system \begin{equation*} \left\{ \begin{array}{ll} - {\rm div} ( a(x, u, \nabla u) ) + A_t (x, u, \nabla u) = G_u(x, u, v) &\hbox{ in $\Omega$,}\\[10pt] -…

We study a nonlinear elliptic equation driven by the degenerate fractional p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e., (p-1)-linear both at infinity and at zero but with different slopes crossing the principal…

We consider the boundary value problem $-\Delta_p u = \lambda c(x) |u|^{p-2}u + \mu(x) |\grad u|^p + h(x)$, $u \in W^{1,p}_0(\Omega) \cap L^{\infty}(\Omega)$, where $\Omega \subset \mathbb R^N$, $N \geq 2$, is a bounded domain with smooth…

In this paper, exploiting variational methods, the existence of multiple weak solutions for a class of elliptic Navier boundary problems involving the $p$-biharmonic operator is investigated. Moreover, a concrete example of an application…

We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity \begin{align} \mathfrak{M}\left(\int_{Q}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_{p}^{s}…

We deal with existence of entire solutions for the quasilinear elliptic system of this type {\Delta}_{p}u_{i}+h_{i}(|x|)|\bigtriangledown u_{i}|^{p-1}=a_{i}(|x|)f_{i}(u_1,u_2) on R^{N} (N\geq3, i=1,2) where N-1\geqp>1, {\Delta}_{p} is the…

In this paper, we study the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~\Omega, \\[2mm] u=0\hfill & \mbox{on}~\partial\Omega, \end{array} \right. \] where…

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the following fractional p-Laplace equation (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where $s \in (0,1)$,$ p \geq 2$,$ N \geq 2$,…

In this paper we study an elliptic variational problem regarding the $p$-fractional Laplacian in $\mathbb{R}^N$ on the basis of recent result \cite{Ha1}, which generalizes the nice work \cite{AT,AP,XZR1}, and then give some sufficient…

We establish the existence of multiple sign-changing solutions to the quasilinear critical problem $$-\Delta_{p} u=|u|^{p^*-2}u, \qquad u\in D^{1,p}(\mathbb{R}^{N}),$$ for $N\geq4$, where $\Delta_{p}u:=\mathrm{div}(|\nabla u|^{p-2}\nabla…

We are concerned with a class of second order quasilinear elliptic equations driven by a nonhomogeneous differential operator introduced by C.A. Stuart and whose study is motivated by models in Nonlinear Optics. We establish sufficient…

We study existence, multiplicity and qualitative properties of entire solutions for a noncompact problem related to p-biharmonic type equations with weights. More precisely, we deal with the following family of equations $$ \Delta_{p}^2 u =…

We consider the problem of multiplicity and uniqueness of radial solutions of a nonlinear elliptic equation of the form \begin{eqnarray*} \begin{gathered} \Delta u +f(u)=0,\quad x\in \mathbb{R}^N, N\geq 2, \lim\limits_{|x|\to\infty}u(x)=0.…

We study a mixed boundary value problem for the quasilinear elliptic equation $\mathop{\rm div}\mathcal{A}(x,\nabla u(x))=0$ in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and…