Related papers: Principal eigenvalues for the weighted p-Laplacian…

We investigate the following eigenvalue problem \begin{align*} \begin{cases} -\operatorname{div}\left( L(x) |\nabla u| ^{p-2}\nabla u\right)=\lambda K(x)|u|^{p-2}u \quad \text{in } A_{R_1}^{R_2} , u=0\quad \text{on } \partial A_{R_1}^{R_2}…

We consider an eigenvalue problem of the form \begin{equation*} \left\{\begin{array}{rclll} -\Delta_{p} u -\Delta_{q} u&=& \lambda K(x)|u|^{p-2}u & \mbox{ in } \Omega^e u&=&0\qquad \quad &\mbox{ on } \partial \Omega u(x) &\to& 0 &\mbox{ as…

Let $\Omega\subset\mathbb{R}^{n}$ be a smooth bounded domain and $m\in C(\overline{\Omega})$ be a sign-changing weight function. For $1<p<\infty$, consider the eigenvalue problem $$ \left\{ \begin{array} [c]{ll} -\Delta_{p}u=\lambda…

We study an {\it indefinite weighted eigenvalue problem} for an operator of {\it mixed-type} (that includes both the classical {\it $p$-Laplacian} and the {\it fractional $p$-Laplacian}) in a bounded open subset $\Omega\subset \mathbb{R}^N…

We study an eigenvalue problem for the infinity-Laplacian on bounded domains. We prove the existence of the principal eigenvalue and a corresponding positive eigenfunction. The work also contains existence results when the parameter, in the…

In this paper, we consider the following eigenvalue problem {{l} (|u"|^{p-2}u")"=\lambda m(x)|u|^{p-2}u, x\in (0,1), u(0)=u(1)=u"(0)=u"(1)=0, where $1<p<+\infty$, $\lambda$ is a real parameter and $m$ is sign-changing weight. We prove there…

We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for…

This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear degenerate or singular uniformly elliptic equations posed in a punctured ball, in presence of a singular…

The spectral theory of the p-Laplacian is well developed for classical Dirichlet and Neumann boundary conditions, but the transitional Robin regime on exterior domains remains largely unexplored. This paper studies a weighted p-Laplacian…

This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we…

In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, $$ -\Delta_p^a u-\Delta_q u =\lambda m(x) |u|^{q-2}u \quad \mbox{in} \,\, \R^N, $$ where {$N \geq 2$}, {$1<p, q<N$,…

This article deals with the existence and non-existence of positive solutions for the eigenvalue problem driven by nonhomogeneous fractional $p\& q$ Laplacian operator with indefinite weights $$\left(-\Delta_p\right)^{\alpha}u +…

In this paper, we study the problem of minimizing the first eigenvalue of the $p-$Laplacian plus a potential with weights, when the potential and the weight are allowed to vary in the class of rearrangements of a given fixed potential $V_0$…

In this article we consider the following weighted nonlinear eigenvalue problem for the $g-$Laplacian $$ -\mathop{\text{ div}}\left( g(|\nabla u|)\frac{\nabla u}{|\nabla u|}\right) = \lambda w(x) h(|u|)\frac{u}{|u|} \quad \text{ in…

We study a nonlinear, nonlocal eigenvalue problem driven by the fractional p-Laplacian with an indefinite, singular weight chosen in an optimal class. We prove the existence of an unbounded sequence of positive variational eigenvalues and…

We analyze the behavior of the eigenvalues of the following non local mixed problem $\left\{ \begin{array}{rcll} (-\Delta)^{s} u &=& \lambda_1(D) \ u &\inn\Omega,\\ u&=&0&\inn D,\\ \mathcal{N}_{s}u&=&0&\inn N. \end{array}\right $ Our goal…

Let $(M,g)$ be a compact Riemannian manifold with a boundary of class $\mathscr{C}^{1}$. We are interested in the spectrum of the weighted Laplacian on $M$ with Neumann boundary conditions. More precisely, given $\rho$ and $\sigma$ two…

This paper is concerned with the Dirichlet eigenvalue problem associated to the $\infty$-Laplacian in metric spaces. We establish a direct PDE approach to find the principal eigenvalue and eigenfunctions in a proper geodesic space without…

The mixed principal eigenvalue of $p\,$-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in $L^p$ space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of…

In this paper, we are interested in the spectral properties of the generalised principal eigenvalue of some nonlocal operator. That is, we look for the existence of some particular solution $(\lambda,\phi)$ of a nonlocal operator.…