Three-Order Multipoint Boundary Value Problems for p-Laplacian Operator on Time Scales

Existence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales

In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.

Positive Solutions for Third-Order Nonlinear p-Laplacian m-Point Boundary Value Problems on Time Scales

We study the following third-order p-Laplacian m-point boundary value problems on time scales: φp uΔ∇ ∇ a t f t, u t 0, t ∈ 0, T T, βu 0 − γuΔ 0 0, u T ∑m−2 i 1 aiu ξi , φp u Δ∇ 0 ∑m−2 i 1 biφp u Δ∇ ξi , where φp s is p-Laplacian operator, that is, φp s |s|p−2s, p > 1, φ−1 p φq, 1/p 1/q 1, 0 < ξ1 < · · · < ξm−2 < ρ T . We obtain the existence of positive solutions by using fixed-point theorem i...

Existence of Positive Solutions for Multipoint Boundary Value Problem with p-Laplacian on Time Scales

Triple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian

‎In this paper‎, ‎we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian‎ ‎dynamic equation on time scales‎. ‎We prove the existence at least three positive solutions of the boundary‎ ‎value problem by using the Avery and Peterson fixed point theorem‎. ‎The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly‎. ‎Our results ...

Existence and uniqueness of solutions for p-laplacian fractional order boundary value problems

In this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-Laplacian fractional order differential equations. We use Schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. We include some examples to show the applicability of our results.