Abstract:

In this paper the authors discuss the existence of positive solution to the following even order boundary value problem

(-1)^m y^(2m)₌f(t,y), 0≤t≤1,
a_i+1y⁽²ⁱ⁾ (0)-β_i+1y ⁽²ⁱ⁺¹⁾ (0)=0, γ_i+1y⁽²ⁱ⁾ (1)+δ_i+1y⁽²ⁱ⁺¹⁾ (1)=0,0≤i ≤m-1

Sufficient conditions are obtained for existence of three or arbitrary odd
positive solutions of the above problem by using Leggett-Williams fixed
point theorem.

Key words: Positive solution, Cone, Fixed point, Boundary value problem