Solutions of 2nth Lidstone boundary value problems and dependence on higher order derivatives

Positive Solutions for Higher Order Lidstone Boundary Value Problems. a New Approach via Sperner’s Lemma

Consider the higher order nonlinear scalar differential equations (0.1) x(t) = −f(t, x(t), ..., y(t), ...y(2(n−1))(t)), 0 ≤ t ≤ 1 where f ∈ C([0, 1] × R+, R+), R+ = [0,∞) associated to the Lidstone boundary conditions (0.2) x(0) = 0 = x(1), (0.3) x(0) = 0 = x(1). Existence of a solution of boundary value Problems (BVP) (0.1)-(0.2) such that x(t) > 0, 0 < t < 1, i = 0, 1, ..., n− 1 are given, un...

Finite spectrum of 2nth order boundary value problems

For any even positive integer 2n and any positive integermwe construct a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most (2n − 1)m + 1 eigenvalues. Our main result reduces to previously known results for the cases n = 1 and n = 2. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n(m + 1)...

Positive Solutions for Third-Order Boundary-Value Problems with the Integral Boundary Conditions and Dependence on the First-Order Derivatives

Third-order boundary-value problems for differential equation play a very important role in a variety of different areas of applied mathematics and physics. Recently, third-order boundary-value problems have been many scholars’ research object. For example, heat conduction, chemical engineering, underground water flow, thermoelasticity, and plasma physics can produce boundary-value problems wit...

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems

Positive Solutions of Complementary Lidstone Boundary Value Problems

Positive Solutions of Complementary Lidstone Boundary Value Problems Ravi P. Agarwal and Patricia J. Y. Wong Department of Mathematics, Texas A&M University – Kingsville, Kingsville, TX 78363, USA. e-mail: [email protected]; Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia. School of Electrical and Electronic Engineering, Nanyang Technological...