Related papers: Nonlinear and Nonlocal Eigenvalue Problems

In this paper, we consider nonlinearly perturbed Legendre differential equations subject to the usual boundary conditions. For such problems we establish sufficient conditions for the existence of solutions and in some cases we provide a…

We consider a class of elliptic and parabolic problems, featuring a specific nonlocal operator of fractional-laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely…

A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…

We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.

We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…

In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…

This paper is concerned with eigenvalue problems for non-symmetric elliptic operators with large drifts in bounded domains under Dirichlet boundary conditions. We consider the minimal principal eigenvalue and the related principal…

In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…

We study the overdetermined problem for a large family of non-local operators given by generators of subordinate Brownian motions. In particular, this family includes the fractional Laplacian, relativistic stable operators etc. We consider…

In this article, we examine two double-phase variable exponent problems, each formulated within a distinct framework. The first problem is non-variational, as the nonlinear term may depend on the gradient of the solution. The first main…

We discuss an eigenvalue problem which arises in the studies of asymptotic stability of a self-similar attractor in the sigma model. This problem is rather unusual from the viewpoint of the spectral theory of linear operators and requires…

In this paper, we investigate condition numbers of eigenvalue problems of matrix polynomials with nonsingular leading coefficients, generalizing classical results of matrix perturbation theory. We provide a relation between the condition…

We prove the existence and multiplicity of weak solutions for a mixed local-nonlocal problem at resonance. In particular, we consider a not necessarily positive operator which appears in models describing the propagation of flames. A…

A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…

We study local regularity properties of linear, non-uniformly parabolic finite-difference operators in divergence form related to the random conductance model on $\mathbb Z^d$. In particular, we provide an oscillation decay assuming only…

We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this…

We study the perturbation by a critical term and a $(p-1)$-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the…

In this article we study the stability problem for positive quaternion-K\"ahler manifolds. We give a description of infinitesimal Einstein deformations and destabilising directions in terms of Laplace eigenfunctions and a special class of…

In this paper we study a family of operators dependent on a small parameter $\epsilon > 0$, which arise in a problem in fluid mechanics. We show that the spectra of these operators converge to N as $\epsilon \to 0$, even though, for fixed…

We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These…