Related papers: Multiple positive radial solutions for Neumann ell…
We consider a nonautonomous semilinear elliptic problem where the power nonlinearity is multiplied by a discontinuous coefficient that equals one inside a bounded open set $\Omega$ and it equals minus one in its complement. In the slightly…
Let $\Omega\subset\mathbb R^{n}\ (n\geq2)$ be either an open ball $B_R$ centred at the origin or the whole space. We study the existence of positive, radial solutions of quasilinear elliptic systems of the form \begin{equation*} \left\{…
In this paper, we study the existence of positive entire large and bounded radial positive solutions for a nonlinear system. Our results give an answer of the question raised in [11].
The focus of this study is on exploring some qualitative properties of solutions to a class of semilinear elliptic problems in bounded domains, where the boundary conditions depend non-locally on the unknown solution at specified interior…
We classify positive solutions to a class of quasilinear equations with Neumann or Robin boundary conditions in convex domains. Our main tool is an integral formula involving the trace of some relevant quantities for the problem. Under a…
The paper deals with positive radial solutions to a nonlinear elliptic equation with singular and decaying potential, for which several existence and nonexistence results are known, resting upon suitable compatibility conditions between the…
We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…
In this paper we are interested in positive classical solutions of \begin{equation} \label{eqx} \left\{\begin{array}{ll} -\Delta u = a(x) u^{p-1} & \mbox{ in } \Omega, \\ u>0 & \mbox{ in } \Omega, \\ u= 0 & \mbox{ on } \pOm, \end…
In this paper, we are concerned with the existence of nonnegative solutions for a nonlinear elliptic system. Our results are obtained by an application of the Arzela--Ascoli theorem.
We consider the fully nonlinear problem \begin{equation*} \begin{cases} -F(x,D^2u)=|u|^{p-1}u & \text{in $\Omega$}\\ u=0 & \text{on $\partial\Omega$} \end{cases} \end{equation*} where $F$ is uniformly elliptic, $p>1$ and $\Omega$ is either…
In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on $\R^N$. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative.…
We analyze existence, multiplicity and oscillatory behavior of positive radial solutions to a class of quasilinear equations governed by the Lorentz-Minkowski mean curvature operator. The equation is set in a ball or an annulus of $\mathbb…
This paper is concerned with the following system of elliptic equations {equation*} \{{array}{ll} -\Delta u+u= F_u(|x|,u,v), & \hbox{} -\Delta v+v=- F_v(|x|,u,v), & \hbox{} \,\,\,\,\,u,v\in H^1(\mathbb{R}^N). & \hbox{} {array}. {equation*}…
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…
We consider a nonlinear Neumann elliptic inclusion with a source (reaction term) consisting of a convex subdifferential plus a multivalued term depending on the gradient. The convex subdifferential incorporates in our framework problems…
We study the stability of radial solutions of the semilinear elliptic equation $\Delta u +f(u)=0$ in ${\bf R^N}$, where $N \geq 3$ and $f$ is a general superciritical nonlinearity. We give a classification of the solution structures with…
We are concerned with positive radial solutions of the inhomogeneous elliptic equation $\Delta u+K(|x|)u^p+\mu f(|x|)=0$ on $\mathbb{R}^N$, where $N\ge 3$, $\mu>0$ and $K$ and $f$ are nonnegative nontrivial functions. If $K(r)\sim…
In this paper we obtain the existence of bounded positive entire radial solutions for the following nonlinear elliptic problem with a special nonlinear gradient term -\triangle_{p}u-b(x)|\nablau|^{p-1}=a(x)f(u), x\inR^{N} (N\geq3),…
We study semilinear elliptic equations \begin{equation*} \begin{cases} -\Delta u = f(u) & \text{in } \Omega, \\ \partial_\nu u = 0 & \text{on } \partial\Omega, \end{cases} \end{equation*} with homogeneous Neumann boundary conditions in…
We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and…