This paper deals with boundary value problems for nonlinear monotone potential operators. An analysis of the nonlinear (monotone potential) Sturm–Liouville operator Au := − ( k((u′)2)u′(x) )′+q(x)u(x), x ∈ (a, b) shows that the potential of this operator as well as the potential of related boundary value problems play an important role not only for solvability of these problems, but also for li...

Recently a great deal of interest has been focused on the application of HPM for the solution of many different problems. The technique has been applied with great success to obtain the solution of a large variety of nonlinear problems in both ordinary and partial differential equations and integro-differential equations[1-10]. In this work we apply HPM to approximate eigenvalues and eigenfunct...

‎this paper deals with the singular sturm-liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of sturm-liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

where the potentials are given functions. Under various boundary conditions, Sturm and Liouville established that solutions of problem (1) can exist only for particular values of the real parameter λ, which is called an eigenvalue. Relevant examples of linear Sturm-Liouville problems are the Bessel equation and the Legendre equation. The classical Sturm-Liouville theory does not depend upon the...