Related papers: Asymptotic formulas for eigenvalues and eigenfunct…
The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.
We derive a new Lyapunov type inequality for a boundary value problem involving both left Riemann--Liouville and right Caputo fractional derivatives in presence of natural conditions. Application to the corresponding eigenvalue problem is…
In this paper, further to the point interaction method for inverse Sturm-Liouville problems on finite intervals firstly proposed in our previous work, we will continue to generalize this method to the inverse eigenvalue problems for…
In this paper, Sturm-Liouville problem for difference equations is considered with potential function q(n). The representations of solutions are obtained by variation of parameters method. These solutions are proved, using summation by…
In this paper, we propose a review of the free boundary formulation for BVPs defined on semi-infinite intervals. The main idea and theorem are illustrated, for the reader convenience, by using a class of second-order BVPs. Moreover, we are…
The transmission eigenvalues corresponding to the half-line Schr\"odinger equation with the general selfadjoint boundary condition is analyzed when the potential is real valued, integrable, and compactly supported. It is shown that a…
The aim of this article is to analyze the asymptotic behaviour of the eigenvalues of elliptic operators in divergence form with mixed boundary type conditions for domains that become unbounded in several directions, while they stay bounded…
We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.
The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds justify the existence of an infinite set of interior…
Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…
In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm-Liouville problem with discontinuities at two points. The problem contains an eigenparameter in the one of boundary conditions. For…
We discuss, via a version of the Birkhoff-Kellogg theorem, the existence of positive and negative eigenvalues of Hammerstein integral equations with sign-changing nonlinearities and functional terms. The corresponding eigenfunctions have a…
The inverse spectral problem is studied for the Sturm-Liouville operator with a complex-valued potential and arbitrary entire functions in one of the boundary conditions. We obtain necessary and sufficient conditions for uniqueness, and…
Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions.
We study Sturm--Liouville differential operators on the time scales consisting of a finite number of isolated points and segments. In a previous paper it was established that such operators are uniquely determined by their spectral…
We consider a class of self-adjoint Sturm-Liouville problems with rational functions of the spectral parameter in the boundary conditions. The uniform stability for direct and inverse spectral problems is proved for the first time for…
In the present review we deal with the recently introduced method of spectral parameter power series (SPPS) and show how its application leads to an explicit form of the characteristic equation for different eigenvalue problems involving…
Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. We consider the case in which the elastic interface is clamped at the lateral walls of a closed trough and thus encloses…
In the paper, we use $\mathrm{U}(2)$, the group of $2\times 2$ unitary matices, to parameterize the space of all self-adjoint boundary conditions for a fixed Sturm-Liouville equation on the interval $[0,1]$. The adjoint action of…
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…