Positive Solutions of Complementary Lidstone Boundary Value Problems

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems

Dynamic Systems and Applications 19 (2010) 113-124 LIDSTONE BOUNDARY VALUE PROBLEMS WITH SIGN-CHANGING NONLINEAR TERMS AND HIGHER ORDER DERIVATIVES

By employing topological degree theory, this paper investigates the existence of at least one nontrivial solutions for Lidstone boundary value problems with sign-changing nonlinear term and higher order derivatives. Meanwhile, one example is worked out to demonstrate the main result.

Triple Positive Symmetric Solutions for a Lidstone Boundary Value Problem

In this paper, we consider the Lidstone boundary value problem (−1)y = f(y(t)), 0 ≤ t ≤ 1, y(0) = 0 = y(1), 0 ≤ i ≤ m − 1, where f : R→ [0,∞). Growth conditions are imposed on f and inequalities involving the Green’s function for this problem are used which enable us to apply the Leggett-Williams Fixed Point Theorem for cones in ordered Banach spaces. This in turn yields the existence of at lea...

Eigenvalues of complementary Lidstone boundary value problems

where l > 0. The values of l are characterized so that the boundary value problem has a positive solution. Moreover, we derive explicit intervals of l such that for any l in the interval, the existence of a positive solution of the boundary value problem is guaranteed. Some examples are also included to illustrate the results obtained. Note that the nonlinear term F depends on y’ and this deriv...

A discrete fourth-order Lidstone problem with parameters

Keywords: Difference equations Boundary value problems Symmetric Green's function Fixed points Fourth-order Discrete Beam Lidstone Semipositone a b s t r a c t Various existence, multiplicity, and nonexistence results for nontrivial solutions to a non-linear discrete fourth-order Lidstone boundary value problem with dependence on two parameters are given, using a symmetric Green's function appr...