Positive solutions of singular nonlinear boundary value problems

Positive solutions for nonlinear singular boundary value problems

We discuss the existence of positive solutions for singular secondorder boundary value problems x′′ = μf (t, x, x′), ax(0) − bx′(0) = k ≥ 0, x′(∞) = 0, where f may be singular at x = 0 and x′ = 0 and can change sign. Via fixed point theory, we establish the existence of positive solutions under some conditions on f . Our results deal with the situation where the solutions approach the singulari...

Solutions of Nonlinear Singular Boundary Value Problems

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

Positive Solutions for a Class of Singular Boundary-value Problems

This paper concerns the existence and multiplicity of positive solutions for Sturm-Liouville boundary-value problems. We use fixed point theorems and the sub-super solutions method to two solutions to the problem studied. Introduction Consider the boundary-value problem Lu = λf(t, u), 0 < t < 1 αu(0)− βu′(0) = 0, γu(1) + δu′(1) = 0, (0.1) where Lu = −(ru′)′ + qu, r, q ∈ C[0, 1] with r > 0, q ≥ ...

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems

Positive Solutions for a Class of Singular Boundary-value Problems

Using regularization and the sub-super solutions method, this note shows the existence of positive solutions for singular differential equation subject to four-point boundary conditions.