In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...

This paper deals with a class of nonlinear fractional Sturm–Liouville boundary value problems. Each sub equation in the system is partial including second kinds Fredholm integral and p-Laplacian operator, simultaneously. Infinitely many solutions are derived due to perfect involvements calculus theory variational methods some simpler more easily verified assumptions.

Keywords: Inverse coefficient problem (ICP) Lie-group adaptive method (LGAM) Leading coefficient Inverse Sturm–Liouville operator Iterative method a b s t r a c t We consider an inverse problem for identifying a leading coefficient a(x) in À(a(x)y 0 (x)) 0 + q(x)y(x) = H(x), which is known as an inverse coefficient problem for the Sturm–Liouville operator. We transform y(x) to u(x, t) = (1 + t)...

The purpose of this paper is fourfold: (1) to introduce and study a second order PDE, determined accidentally by a Riemann wave, reflecting the connection between oriented parallelograms area and sectional curvature on Riemannian manifolds; (2) to introduce and study the asymptotic behavior of oriented parallelograms area controlled by the sectional curvature; (3) to study some partial differen...

Abstract In this article, we focus on the scattering analysis of Sturm-Liouville type singular operator including an impulsive condition and turning point. classical literature, there are plenty papers considering positive values weight function in both continuous discontinuous cases. However, article differs from others terms appearing at We generate function, resolvent operator, discrete spec...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm–Liouville equation on [0, a] with real potential q(x) ∈ L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [ 3 , a] and 3) the potential on [0, a 3 ]. The aim is to find the potential on [ 3 , a].

In many inverse problems, the measurement operator, which maps objects of interest to available measurements, is a smoothing (regularizing) operator. Its inverse is therefore unbounded and as a consequence, only the low frequency component of the object of interest is accessible from inevitably noisy measurements. In many inverse problems however, the neglected high frequency component may sign...

We consider the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t), u′(t)) = λu(t), u(t) > 0, t ∈ I := (−1/2, 1/2), u(±1/2) = 0, where f(x, y) = |x|p−1x − |y|m, p > 1, 1 ≤ m < 2 are constants and λ > 0 is an eigenvalue parameter. To understand well the global structure of the bifurcation branch of positive solutions in R+ ×Lq(I) (1 ≤ q < ∞) from a viewpoint of inverse problems, we establish the...

In this paper we define the Evans function for Sturm-Liouville problems. We show that the Evans function is analytic in the spectral parameter, has zeros in one-to-one correspondence with the eigenvalues, and is under certain conditions what we call conjugate symmetric. We conclude by showing that the Evans function can be used to track the movement of the eigenvalues as the coefficients in the...