Existence of Positive Solutions for Higher Order (p,q)‎-Laplacian Two-Point Boundary Value Problems

Abstract EN

We derive sufficient conditions for the existence of positive solutions to higher order (p,q)-Laplacian two-point boundary value problem, (-1)m1+n1-1[ϕp(u(2m1)(t))](n1)=f1(t,u(t),v(t)), t∈[0,1], (-1)m2+n2-1[ϕq(v(m2)(t))](2n2)=f2(t,u(t),v(t)), t∈[0,1], u(2i)(0)=0=u(2i)(1), i=0,1,2,…,m1-1, [ϕp(u(2m1)(t))]at t=0(j)=0, j=0,1,…,n1-2; [ϕp(u(2m1)(1))]=0, [ϕq(v(m2)(t))]at t=0(2i)=0=[ϕq(v(m2)(t))]at t=1(2i), i=0,1,…,n2-1, v(j)(0)=0, j=0,1,2,…,m2-2, and v(1)=0, where f1,f2 are continuous functions from [0,1]×ℝ2 to [0,∞), m1,n1,m2,n2∈ℕ and 1/p+1/q=1.

We establish the existence of at least three positive solutions for the two-point coupled system by utilizing five-functional fixed point theorem.

And also, we demonstrate our result with an example.