相关论文: Fu/v cik Spectrum for the Neumann Problem with Ind…
This paper is devoted to the study of the Fu/v cik spectrum with indefinite weights in the one-dimensional case.
In this paper, we study the Fu\v{c}ik spectrum for the operator with rapidly increasing weight, which is defined as a set $\Sigma$ comprising those $(\alpha, \beta) \in \mathbb{R}^2$ such that \begin{equation*} \left\{\begin{array}{l} L…
In this work we consider the Fu\u{c}ik problem for a family of weights depending on $\ve$ with Dirichlet and Neumann boundary conditions. We study the homogenization of the spectrum. We also deal with the special case of periodic…
Spectral asymptotics of the Sturm-Liouville problem with an arithmetically self-similar singular weight is considered. Previous results by A. A. Vladimirov and I. A. Sheipak, and also by the author, rely on the spectral periodicity…
We consider a singular Sturm-Liouville expression with the indefinite weight sgn x. To this expression there is naturally a self-adjoint operator in some Krein space associated. We characterize the local definitizability of this operator in…
Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral…
Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite…
In this article, we study the Fu\v{c}ik spectrum of fractional Laplace operator which is defined as the set of all $(\al,\ba)\in \mb R^2$ such that \begin{equation*} \quad \left. \begin{array}{lr} \quad (-\De)^s u = \al u^{+} - \ba u^{-} \;…
Spectral asymptotics of the Neumann problem for the Sturm-Liouville equation with generalized derivative of a self-similar generalized Cantor type function as a weight are considered. The spectrum is shown to have a periodicity property for…
In this work, we investigate the spectral problem $Au = {\lambda}u$ where $A$ is a fractional elliptic operator involving left- and right-sided Riemann-Liouville derivatives. These operators are nonlocal and nonsymmetric, however, share…
Considering the radial nonlinear Schrodinger equation - \Delta u + V(x)u = g(x,u) in R^N, N \geq 3 we aim to find a radial nontrivial solution for it, where V changes sign ensuring this problem is indefinite and g is an asymptotically…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…
In this paper, we investigate the Fu\v{c}\'{i}k spectrum $\Sigma_L$ associated with the logarithmic Laplacian. This spectrum is defined as the set of all pairs $(\alpha,\beta) \in \mathbb{R}^2$ for which the problem \[ L_\Delta u = \alpha…
Spectral problem for a family of periodic Sturm--Liouville problems \[ u''+\lambda^2(a(x)-a)u=0 \] depending on the parameter (a\in\mathbb R) is considered. An interpolation formula describing the behaviour of the branches of the spectrum…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
In this paper, by using the similar methods of [O. Sh. Mukhtarov and M. Kadakal, Some spectral properties of one Sturm-Liouville type problem with discontinuous weight, Siberian Mathematical Journal, 46 (2005) 681-694] we extend some…
The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…
In this paper we present a new approach to the spectral theory of {\it non-uniformly continuous} functions and a new framework for the Loomis-Arendt-Batty-Vu theory. Our approach is direct and free of $C_0$-semigroups, so the obtained…
Spectral asymptotics of the Sturm-Liouville problem with a singular self-conformal weight measure is considered. A stronger version of the bounded distortion property is assumed for the conformal iterated function system corresponding to…
We consider the nonlinear equation $$-u'' = f(u) + h , \quad \text{on} \quad (-1,1),$$ where $f : {\mathbb R} \to {\mathbb R}$ and $h : [-1,1] \to {\mathbb R}$ are continuous, together with general Sturm-Liouville type, multi-point boundary…