We consider the existence of positive solutions for a class of discrete second-order four-point boundary value problem with p-Laplacian. Using the well known Krasnosel’skii’s fixed point theorem, some new existence criteria for positive solutions of the boundary value problem are presented.

Uniqueness of and numerical techniques for the inverse Sturm-Liouville problem with eigenparameter dependent boundary conditions will be discussed. We will use a Gel’fand-Levitan technique to show that the potential q in u00 þ qu 1⁄4 u, 0 < x < 1 uð0Þ 1⁄4 0, ða þ bÞuð1Þ 1⁄4 ðc þ d Þu0ð1Þ can be uniquely determined using spectral data. In the presence of finite spectral data, q can be reconstruc...

in this work, byemploying the leggett-williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

In this paper, we study the second-order nonlinear singular Sturm-Liouville boundary value problems with Riemann-Stieltjes integral boundary conditions    −(p(t)u(t)) + q(t)u(t) = f(t, u(t)), 0 < t < 1, α1u(0)− β1u (0) = ∫ 1 0 u(τ)dα(τ), α2u(1) + β2u (1) = ∫ 1 0 u(τ)dβ(τ), where f(t, u) is allowed to be singular at t = 0, 1 and u = 0. Some new results for the existence of positive solu...

*Correspondence: [email protected] Department of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh, 11586, Saudi Arabia Abstract In this article, we extend fractional calculus with nonsingular exponential kernels, initiated recently by Caputo and Fabrizio, to higher order. The extension is given to both left and right fractional derivatives and integrals. ...

The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on the problem. An expression for the derivative of the n-th eigenvalue with respect to a given parameter: an endpoint, a boundary condition constant, a coefficient or weight function, is found.

Given any self-adjoint realization S of a singular Sturm-Liouville (S-L) problem, it is possible to construct a sequence {Sr} of regular S-L problems with the properties (i) every point of the spectrum of S is the limit of a sequence of eigenvalues from the spectrum of the individual members of {Sr} (ii) in the case when S is regular or limit-circle at each endpoint, a convergent sequence of ei...

The author studies the inverse scattering problem for a boundary value problem of a generalized one dimensional Schrödinger type with a discontinuous coefficient and eigenparameter dependent boundary condition. The solutions of the considered eigenvalue equation is presented and its scattering function that satisfies some properties is induced. The discrete spectrum is studied and the resolvent...