Related papers: An eigenvalue problem for a generalized polyharmon…

We study singular perturbations of eigenvalues of the polyharmonic operator on bounded domains under removal of small interior compact sets. We consider both homogeneous Dirichlet and Navier conditions on the external boundary, while we…

In this paper we study the maximum principle, the existence of eigenvalue and the existence of solution for the Dirichlet problem for operators which are fully-nonlinear, elliptic but presenting some singularity or degeneracy which are…

Let $\Omega$ be a bounded domain with $C^2$-smooth boundary in an $n$-dimensional oriented Riemannian manifold. It is well-known that for the bi-harmonic equation $\Delta^2 u=0$ in $\Omega$ with the $0$-Dirichlet boundary condition, there…

In H\"ormander inner product spaces, we investigate initial-boundary value problems for an arbitrary second order parabolic partial differential equation and the Dirichlet or a general first-order boundary conditions. We prove that the…

In this paper we study the Dirichlet eigenvalue problem $$ -\Delta_p u-\Delta_{J,p}u =\lambda|u|^{p-2}u \quad \text{ in } \Omega,\quad u=0 \quad\text{ in } \Omega^c=\mathbb{R}^N\setminus\Omega. $$ Here $\Delta_p u$ is the standard local…

In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation $(-\Delta)^m u=g(u)$, assuming that $g$ has a general subcritical growth at infinity, inspired by Berestycki and Lions…

Let $(\mathbb{X} , d, \mu )$ be a proper metric measure space and let $\Omega \subset \mathbb{X}$ be a bounded domain. For each $x\in \Omega$, we choose a radius $0< \varrho (x) \leq \mathrm{dist}(x, \partial \Omega ) $ and let $B_x$ be the…

We consider an eigenvalue problem for the biharmonic operator with Steklov-type boundary conditions. We obtain it as a limiting Neumann problem for the biharmonic operator in a process of mass concentration at the boundary. We study the…

Let $\Omega$ be a bounded domain in $\mathbb R^2$ with smooth boundary $\partial\Omega$, and let $\omega_h$ be the set of points in $\Omega$ whose distance from the boundary is smaller than $h$. We prove that the eigenvalues of the…

We study the spectral problems associated with the finite-difference operators $H_N = 2 \cosh(p) + V_N(x)$, where $V_N(x)$ is an arbitrary polynomial potential of degree $N$. These systems can be regarded as a solvable deformation of the…

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…

The main scope of this article is to define the concept of principal eigenvalue for fully non linear second order operators in bounded domains that are elliptic and homogenous. In particular we prove maximum and comparison principle, Holder…

In this paper we study an eigenvalue problem for the so called $(p,2)$-Laplace operator on a smooth bounded domain under a nonlinear Steklov type boundary condition, namely \begin{equation} \left\{ \begin{aligned} -\Delta_pu-\Delta u &…

We study the most general class of eigenfunction expansions for abstract normal operators with pure point spectrum in a complex Hilbert space. We find sufficient conditions for such expansions to be unconditionally convergent in spaces with…

We consider nonlinear equations having generalized Orlicz growth (also known as Musielak--Orlicz growth). We prove that if differential operators $\mathcal{A}_i$ converge locally uniformly to an operator $\mathcal{A}$, then the sequence of…

We study the biharmonic equation $\Delta^2 u =u^{-\alpha}$, $0<\alpha<1$, in a smooth and bounded domain $\Omega\subset\RR^n$, $n\geq 2$, subject to Dirichlet boundary conditions. Under some suitable assumptions on $\o$ related to the…

The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…

We study integral operators $\mathcal{L}u(x)=\int_{\mathbb{R^N}}\psi(u(x)-u(y))J(x-y)\,dy$ of the type of the fractional $p$-Laplacian operator, and the properties of the corresponding Orlicz and Sobolev-Orlicz spaces. In particular we show…

We study the problem of approximating plurisubharmonic functions on a bounded domain $\Omega$ by continuous plurisubharmonic functions defined on neighborhoods of $\bar\Omega$. It turns out that this problem can be linked to the problem of…

We study the asymptotic behaviour of eigenvalues and eigenfunctions of a boundary value problem for the Sturm-Liouville operator with general boundary conditions and the weight function perturbed by the so-called $\delta'$-like sequence…