Related papers: On an eigenvalue problem associated with mixed ope…
In this paper, we study the existence, nonexistence and multiplicity of positive solutions to the problem given by \begin{equation*} \label{1} \left\{\begin{split} \mathcal{L}u\: &= \lambda u^{q} + u^{p}, \quad u>0 ~~ \text{in} ~\Omega,…
In this article, we are concerned with the eigenvalue problem driven by the mixed local and nonlocal $p$-Laplacian operator having the interpolated Hardy term \begin{equation*} \mathcal{T}(u) :=- \Delta_p u + (- \Delta_p)^s u - \mu…
In a rectangular domain, a boundary-value problem is considered for a mixed-type equation with a regularized Caputo-like counterpart of hyper-Bessel differential operator and the bi-ordinal Hilfer's fractional derivative. Using the method…
The aim of this paper is to prove multiplicity of solutions for nonlocal fractional equations modeled by $$ \left\{ \begin{array}{ll} (-\Delta)^s u-\lambda u=f(x,u) & {\mbox{ in }} \Omega\\ u=0 & {\mbox{ in }} \mathbb{R}^n\setminus…
In this paper we study the nonlinear Neumann boundary value problem of the following equations -\text{div}(|\nabla u|^{p_{1}(x)-2}\nabla u)-\text{div}(|\nabla u|^{p_{2}(x)-2}\nabla u)+|u|^{p_{1}(x)-2}u+|u|^{p_{2}(x)-2}u=\lambda f(x,u) in a…
In this paper, we show the existence of a sequence of eigenvalues for a Dirichlet problem involving two mixed fractional operators with different orders. We provide lower and upper bounds for the sum of the eigenvalues. Applications of…
Non-local boundary conditions for Euclidean quantum gravity are proposed, consisting of an integro-differential boundary operator acting on metric perturbations. In this case, the operator P on metric perturbations is of Laplace type,…
We describe a highly efficient numerical scheme for finding two-sided bounds for the eigenvalues of the fractional Laplace operator (-Delta)^{alpha/2} in the unit ball D in R^d, with a Dirichlet condition in the complement of D. The…
In this work, a mixed problem for a time-fractional equation with a delayed argument and pseudodifferential operators related to Laplace operators with non-local boundary conditions in Sobolev classes is studied. The solutions to the…
We study the family of operators $\{\mathcal{R}_a\}_{a\in [0,+\infty)}$ associated to the Robin-type problems in a bounded domain $\Omega\subset\mathbb{R}^2$ $$ \begin{cases} -\Delta u = f & \text{in } \Omega, \\ 2 \bar \nu \partial_{\bar…
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 &…
This paper examines the Laplace equation with mixed boundary conditions, the Neumann and Steklov boundary conditions. This models a container with holes in it, like a pond filled with water but partly covered by immovable pieces on the…
In this work we study the following fractional critical problem $$ (P_{\lambda})=\left\{\begin{array}{ll} (-\Delta)^s u=\lambda u^{q} + u^{2^*_{s}-1}, \quad u{>}0 & \mbox{in} \Omega\\ u=0 & \mbox{in} \RR^n\setminus \Omega\,,…
Nonlocal models and their associated theories have been extensively investigated in recent years. Among these, nonlocal versions of the classical Laplace operator have attracted the most attention, while higher-order nonlocal operators have…
We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator under consideration is obtained as a superposition of operators…
We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…
In this paper we consider a Robin-type Laplace operator on bounded domains. We study the dependence of its lowest eigenvalue on the boundary conditions and its asymptotic behavior in shrinking and expanding domains. For convex domains we…
This paper deals with the homogenization of a mixed boundary value problem for the Laplace operator in a domain with locally periodic oscillating boundary. The Neumann condition is prescribed on the oscillating part of the boundary, and the…
The present paper studies the non-local fractional analogue of the famous paper of Brezis and Nirenberg in [4]. Namely, we focus on the following model, $$\begin{align*}\left(\mathcal{P}\right) \begin{cases} \left(-\Delta\right)^s u-\lambda…
We consider a singular perturbed eigenvalue problem for Laplace operator in a cylinder with frequent interchange of type of boundary condition on a lateral surface. These boundary conditions are prescribed by partition of lateral surface in…