Multiple symmetric positive solutions for a second order boundary value problem

Multiple Symmetric Positive Solutions for a Second Order Boundary Value Problem

For the second order boundary value problem, y′′ + f(y) = 0, 0 ≤ t ≤ 1, y(0) = 0 = y(1), where f : R → [0, ∞), growth conditions are imposed on f which yield the existence of at least three symmetric positive solutions.

Multiple positive solutions for a second-order boundary value problem with integral boundary conditions

where α and β are nonnegative constants. Boundary value problems of ordinary differential equations arise in kinds of different areas of applied mathematics and physics. Many authors have studied two-point, threepoint, multi-point boundary value problems for second-order differential equations extensively, see [–] and the references therein. In recent years, boundary value problems with integ...

Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

Positive Solutions to a Singular Second Order Boundary Value Problem

In this paper, we establish some criteria for the existence of positive solutions for certain two point boundary value problems for the singular nonlinear second order equation −(ru ) + qu = λf (t, u ) on a time scale T. As a special case when T = R, our results include those of Erbe and Mathsen [11]. Our results are new in a general time scale setting and can be applied to difference and q-dif...

Positive Solutions to a Second-Order Discrete Boundary Value Problem