International Journal of Computational and Applied Mathematics
  • Year: 2010
  • Volume: 5
  • Issue: 2

Multiple Positive Solutions for Nonlinear Third Order Three-Point Boundary Value Problems on Time Scales

  • Author:
  • S. Nageswara Rao1, A. Kameswara Rao2
  • Total Page Count: 16
  • Page Number: 141 to 156

1Dept. of Mathematics, Sri Prakash College of Engg., Tuni, A.P., India.

2Dept. of Applied Mathematics, Andhra University, Visakhapatnam, India.

1991 Mathematics Subject Classification: Primary - 34B99; secondary – 39A99.

Abstract

We consider third order nonlinear three-point boundary value problem on time scales, yΔΔΔ (t) + f(t, y(t)) = 0, t ∈[a,c]T subject to the boundary conditions y(a)−0, yΔ (b) = 0, yΔΔ (σ(c)) = 0.

We establish the existence of at least one positive solution, and existence of at least three positive solutions for the three-point boundary value problem using Krasnosel'skii and Leggett-Williams fixed point theorems on a cone.

Keywords

Time scales, boundary value problem, positive solution, cone, multiple positive solution