Related papers: Nonlinear and Nonlocal Eigenvalue Problems
In this study, we address the eigenvalue problem given by: \begin{equation*} \begin{cases} -\Div (w\nabla u_i)=\la_iu_i &\text{in } \Om\subset \mathbb{R}^n,\\ u_i=0 &\text{on } \pt \Om, \end{cases} \end{equation*} where $w > 0$ within $\Om$…
In this paper, we introduce the fractional anisotropic Orlicz-Sobolev spaces, and by using some variational methods, we establish the existence or non-existence of eigenvalues of fractional anisotropic problems involving a nonlocal…
In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered…
In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
The continuous dependence of solutions to certain (non-autonomous, partial, integro-differential-algebraic, evolutionary) equations on the coefficients is addressed. We give criteria that guarantee that convergence of the coefficients in…
In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly…
In this paper we prove a variation of constants formula for a non autonomous and non homogeneous Cauchy problems whenever the linear part is not densely defined and is not a Hille-Yosida operator. By using this variation of constants…
Initial-boundary value problems for the linear Zakharov-Kuznetsov equation posed on bounded rectangles are considered. Spectral properties of a stationary operator are studied in order to show that the evolution problem posed on a bounded…
The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…
We consider the class of two-lag linear delay differential equations and develop a series expansion to solve for the roots of the nonlinear characteristic equation. Supporting numerical results are presented along with application of our…
In this paper we investigate a minimization problem related to the principal eigenvalue of the $s$-wave Schr\"{o}dinger operator. The operator depends nonlinearly on the eigenparameter. We prove the existence of a solution for the…
We consider the problem of discrete-time signal denoising, focusing on a specific family of non-linear convolution-type estimators. Each such estimator is associated with a time-invariant filter which is obtained adaptively, by solving a…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
We prove the existence of minimizers for functionals defined over the class of convex domains contained inside a bounded set D of R^N and with prescribed volume. Some applications are given, in particular we prove that the eigenvalues of…
We investigate the existence of strong solutions to a general class of doubly multivalued and nonlinear evolution equations of second order. The multivalued operators are generated by the subdifferential of nonsmooth potentials that live in…
We show an existence of a weak solution of a degenerate and/or singular semilinear elliptic boundary value (nonhomogeneous) problem lying between a given weak subsolution and a given weak supersolution. It has been applied for an existence…
Motivated by the problems of analytic hypoellipticity, we show that a special family of compact non self-adjoint operators has a non-zero eigenvalue. We recover old results by Christ,Hanges, Himonas, Pham-The-Lai and Robert proved by using…
Eigenvalues inequalities involving (log) convex/concav functions and Hermitian matrices, positive unital maps are considered. Simple proofs of Bhatia-Kittaneh inequality and Naimark dilation theorem are given.
We prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for perturbed Hammerstein integral equations. Our approach is topological and relies on the classical fixed point index. Some of the…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…