A Sturm Type Comparison Theorem for Nonlinear Problems

A Sturm Type Comparison Theorem for Nonlinear Problems

A Nonlinear Sturm–Picone Comparison Theorem for Dynamic Equations on Time Scales

The authors derive an analog of the well-known Picone identity but for nonlinear dynamic equations on time scales. As a consequence, they obtain a nonlinear comparison theorem in the spirit of the classical Sturm–Picone comparison theorem. Comparison results yielding the nonoscillation of all solutions of nonlinear equations are also obtained. AMS subject classification: 34C10, 34C15, 39A11.

Inverse Spectral Problems for Nonlinear Sturm-liouville Problems

This paper concerns the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t)) = λu(t), u(t) > 0, t ∈ I := (0, 1), u(0) = u(1) = 0, where λ is a positive parameter. We try to determine the nonlinear term f(u) by means of the global behavior of the bifurcation branch of the positive solutions in R+ × L2(I).

Spectral asymptotics for inverse nonlinear Sturm-Liouville problems

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...

Adomian Decomposition Method for Nonlinear Sturm-liouville Problems

In this paper the Adomian decomposition method is applied to the nonlinear SturmLiouville problem −y + y(t) = λy(t), y(t) > 0, t ∈ I = (0, 1), y(0) = y(1) = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.