System of singular second-order differential equations with integral condition on the positive half-line (original) (raw)

Existence of Positive Solutions for Singular Second-orderm-Point Boundary Value Problems

Acta Mathematicae Applicatae Sinica, English Series, 2004

In this paper we consider the existence of at least one positive solution to a class of singular semipositone coupled system of nonlocal boundary value problems. We show that the system possesses at least one positive solution by using fixed point index theory. We remark that to some extent our systems and results generalize and extend some previous works.

Positive solutions for second-order differential equations with singularities and separated integral boundary conditions

Electronic Journal of Qualitative Theory of Differential Equations

We study the existence of positive solutions for second-order differential equations with separated integral boundary conditions. The nonlinear part of the equation involves the derivative and may be singular for the second and third space variables. The result ensures existence of a positive solution when the parameters are in certain ranges. The proof depends on general properties of the associated Green's function and the Krasnosel'skii-Guo fixed point theorem applied to a perturbed Hammerstein integral operator. Both numerical and analytical examples are constructed to illustrate applications of the theorem to a group of equations. The result generalizes previous work.

Positive solutions to a singular second order boundary value problem

International Journal of Mathematical Analysis, 2013

In this paper, we investigate the existence and multiplicity of positive solutions for a singular second order scalar Sturm-Liouville boundary value problem with different values of λ for a function f involve u by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.

Positive solutions of second order boundary value problems

2006

In this paper we investigate the existence of positive solutions of two-point boundary value problems for nonlinear second order differential equations of the form (py ) (t) + q(t)y(t) = f (t, y(t), y (t)), where f is a Carathéodory function, which may change sign, with respect to its second argument, infinitely many times.