Abstract
We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
Highlights
Let T be any time scale such that 0, 1 be subset of T
The concept of dynamic equations on time scales can build bridges between differential and difference equations. This concept gives us unified approach to study the boundary value problems on discrete intervals with uniform step size and real intervals and gives an extended approach to study on discrete case with non uniform step size or combination of real and discrete intervals
We study the existence of positive solutions for the following nonlinear four-point boundary value problem with a p-Laplacian operator: φp xΔ
Summary
Let T be any time scale such that 0, 1 be subset of T. The concept of dynamic equations on time scales can build bridges between differential and difference equations. This concept gives us unified approach to study the boundary value problems on discrete intervals with uniform step size and real intervals and gives an extended approach to study on discrete case with non uniform step size or combination of real and discrete intervals. We study the existence of positive solutions for the following nonlinear four-point boundary value problem with a p-Laplacian operator: φp xΔ ∇ thtft, x t. H1 the function f ∈ C 0, 1 × 0, ∞ , 0, ∞ , H2 the function h ∈ Cld T, 0, ∞ and does not vanish identically on any closed subinterval of ρ 0 , σ 1 and 0 < σ ρ 1 0 h t ∇t
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