Positive Solutions to a Second-Order Discrete Boundary Value Problem

Positive Solutions to a Second-Order Discrete Boundary Value Problem

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...

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.

Three Positive Solutions to a Discrete Focal Boundary Value Problem

We are concerned with the discrete focal boundary value problem ∆3x(t−k) = f(x(t)), x(a) = ∆x(t2) = ∆2x(b+ 1) = 0. Under various assumptions on f and the integers a, t2, and b we prove the existence of three positive solutions of this boundary value problem. To prove our results we use fixed point theorems concerning cones in a Banach space.

Multiple Positive Solutions to a Fourth-order Boundary-value Problem

We study the existence, localization and multiplicity of positive solutions for a nonlinear fourth-order two-point boundary value problem. The approach is based on critical point theorems in conical shells, Krasnosel’skĭı’s compression-expansion theorem, and unilateral Harnack type inequalities.