相关论文: Entire solutions of quasilinear symmetric systems

It is established existence and multiplicity of solution for the following class of quasilinear elliptic problems $$ \left\{ \begin{array}{lr} -\Delta_\Phi u = \lambda a(x) |u|^{q-2}u + |u|^{p-2}u, & x\in\Omega, u = 0, & x \in \partial…

We study the following elliptic system concerning the fractional Laplacian operator $$(- \Delta)^ {s_i} u_i = H_i ( u_1,\cdots,u_m) \ \ \text{in}\ \ \mathbb{R}^n,$$ when $0<s_i<1$, $u_i: \mathbb R^n\to R$ and $H_i$ belongs to…

In this paper, we investigate the existence of solutions for a class of quasilinear elliptic system \begin{eqnarray*} \begin{cases}{ccc} -\mbox{div}(\phi_1(|\nabla u|)\nabla u)+V_1(x)\phi_1(|u|)u=\lambda F_u(x, u,v), \ \ x\in \mathbb R^N,…

We characterize the existence of solutions to the quasilinear Riccati type equation \begin{eqnarray*} \left\{ \begin{array}{rcl} -{\rm div}\,\mathcal{A}(x, \nabla u)&=& |\nabla u|^q + \sigma \quad \text{in} ~\Omega, \\ u&=&0 \quad…

We investigate the existence and nonexistence of positive solutions for the quasilinear elliptic inequality $L_\mathcal{A} u= -{\rm div}[\mathcal{A}(x, u, \nabla u)]\geq (I_\alpha\ast u^p)u^q$ in $\Omega$, where $\Omega\subset \mathbb{R}^N,…

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 analyze the existence of entire radially symmetric solutions for Schrodinger system type {\Delta}_{p_{i}}u_{i}+h_{i}(r)|\nabla u_{i}|^{p_{i}-1}=a_{i}(r)f_{i}(u_1,...,u_{d}) for i=1,...,d on R^{N} where p_{i}>1, d \in…

In this paper we study quasilinear elliptic systems given by \begin{equation*} \begin{aligned} -\Delta_{p_1}u_1 & =-|u_1|^{p_1-2}u_1 \quad && \text{in } \Omega,\newline -\Delta_{p_2}u_2 & =-|u_2|^{p_2-2}u_2 \quad && \text{in }…

It is establish regularity results for weak solutions of quasilinear elliptic problems driven by the well known $\Phi$-Laplacian operator given by \begin{equation*} \left\{\ \begin{array}{cl} \displaystyle-\Delta_\Phi u= g(x,u), &…

Let (M^n,g) be a n-dimensional complete, non-compact and connected Riemannian manifold, with Ricci tensor Ricc_g and sectional curvature Sec_g. Assume Ricc_g\geq (1-n)B^2, and either p>2 and Sec_g(x)=o(dist^2(x,a)) when dist^2(x,a)\to\infty…

In this work, we study a quasilinear elliptic problem involving the 1-laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function $H(\cdot - \beta)$. Our approach is based on an…

We study the quasilinear elliptic inequality $$ -\Delta_m u - \frac{\mu}{|x|^m}u^{m-1} \geq (I_\alpha*u^p)u^q \quad\mbox{ in }\mathbb{R}^N\setminus \overline B_1, N\geq 1, $$ where $p>0$, $q, \mu \in \mathbb{R}$, $m>1$ and $I_\alpha$ is the…

We investigate a class of quasilinear elliptic system involving a nonhomogeneous differential operator which is introduced by C. A. Stuart [Milan J. Math. 79 (2011), 327-341] and depends on not only $\nabla u$ but also $u$. We show that the…

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…

We examine stable solutions of the following symmetric system on a complete, connected, smooth Riemannian manifold $\mathbb{M}$ without boundary, \begin{equation*} -\Delta_g u_i = H_i(u_1,\cdots,u_m) \ \ \text{on} \ \ \mathbb{M},…

In this paper our main goal is to present a new global $L^\infty$-estimate for a general class of quasilinear elliptic equations of the form $$ -div \mathcal{A}(x,u,\nabla u)=\mathcal{B}(x,u,\nabla u) $$ under minimal structure conditions…

In this paper, we study a new class of fully nonlinear uniformly elliptic equations with a so-called harmonic map-like structure, whose model case is given by \begin{equation*} \mathcal{M}^{\pm}_{\lambda,\Lambda}(D^2u) \pm b(x) |Du| \pm…

In this work, we establish global gradient estimates to solutions of quasilinear elliptic models in non-divergence form with general degeneracy law and a Hamiltonian term, given by $$ -\Psi(x, |\nabla…

We establish multiplicity results for the following class of quasilinear problems $$ \left\{ \begin{array}{l} -\Delta_{\Phi}u=f(x,u) \quad \mbox{in} \quad \Omega, \\ u=0 \quad \mbox{on} \quad \partial \Omega, \end{array} \right. \leqno{(P)}…

In this paper we consider the model semilinear Neumann system $$\left\{ \begin{array}{lll} -\Delta u+a(x)u=\lambda c(x) F_u(u,v)& {\rm in} & \Omega,\\ -\Delta v+b(x)v=\lambda c(x) F_v(u,v)& {\rm in} & \Omega,\\ \frac{\partial u}{\partial…