Related papers: Multiple solutions to quasi-linear elliptic Robin …
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these…
We shall prove a multiplicity result for semilinear elliptic problems with a super-critical nonlinearity of the form, \begin{equation}\label{con-c} \left \{ \begin{array}{ll} -\Delta u =|u|^{p-2} u+\mu |u|^{q-2}u, & x \in \Omega\\ u=0, & x…
We present a geometric formula of Poincar\'e type, which is inspired by a classical work of Sternberg and Zumbrun, and we provide a classification result of stable solutions of linear elliptic problems with nonlinear Robin conditions on…
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…
We establish the existence of three solutions for sign-coupled Gierer-Meinhardt type system with Neumann boundary conditions. Two solutions are of opposite constant-sign while the third solution is nodal with synchronous sign components.…
This paper is devoted to the study, with variational technique, of (p,q)-Laplacian equations in presence of general nonlinearities. Especially we obtain the existence result for the zero mass case, which includes a large class of pure power…
This article focuses on a quasilinear wave equation of $p$-Laplacian type: $$ u_{tt} - \Delta_p u - \Delta u_t=0$$ in a bounded domain $\Omega\subset\mathbb{R}^3$ with a sufficiently smooth boundary $\Gamma=\partial\Omega$ subject to a…
In the first part of the article, we give necessary and sufficient conditions for the solvability of a class of nonlinear elliptic boundary value problems with nonlinear boundary conditions involving the q-Laplace-Beltrami operator. In the…
The aim of this paper is the study of existence of solutions for non- linear p-Laplacian difference equations. In the first part, the existence of a nontrivial homoclinic solution for a discrete p-Laplacian problem is proved. The proof is…
In this paper we study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization…
By means of a recent variational technique, we prove the existence of radially monotone solutions to a class of nonlinear problems involving the $p$-Laplace operator. No subcriticality condition (in the sense of Sobolev spaces) is required.
We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$ -\Delta u =|v|^{p-1}v\ \hbox{in}\ \mathbb{R}^N,\ -\Delta v =|u|^{q-1}u\ \hbox{in}\ \mathbb{R}^N,$$ where the…
In this work we establish existence and multiplicity of solutions for elliptic problem with nonlinear boundary conditions under strong resonance conditions at infinity. The nonlinearity is resonance at infinity and the reso- nance phenomena…
We go further in the investigation of the Robin problem $(P_{\alpha})$: $-\Delta u=a(x)u^{q}$ in $\Omega$, $u\geq0$ in $\Omega$, $\partial_{\nu}u=\alpha u$ on $\partial \Omega$; on a bounded domain $\Omega\subset\mathbb{R}^{N}$, with $a$…
We study a partial differential inclusion, driven by the p-Laplacian operator, involving a p-superlinear nonsmooth potential, and subject to Neumann boundary conditions. By means of nonsmooth critical point theory, we prove the existence of…
In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
In this paper we study, in dimension two, the stability of the solutions of some nonlinear elliptic equations with Neumann boundary conditions, under perturbations of the domains in the Hausdorff complementary topology.
In this paper, we prove a maximum principle for the $p$-Laplacian with a sign-changing weight. As an application of this maximum principle, we study the existence of one-sign solutions for a class of quasilinear elliptic problems.
In this paper we study the fractional p(., .)-Laplacian and we introduce the corresponding nonlocal conormal derivative for this operator. We prove basic properties of the corresponding function space and we establish a nonlocal version of…