Wednesday, March 30, 2016

the existence of multiple positive solutions for the third-order p-Laplacian dynamic equation (ϕp(uΔ∇(t)))∇+a(t)f(t,u(t),uΔ(t))=0,t∈[0,T]핋 with the multipoint boundary conditions uΔ(0)=uΔ∇(0)=0,u(T)+B0(∑i=1m−2biuΔ(ξi))=0, where ϕp(u)=|u|p−2u with p>1.

Multiple Positive Solutions of m-Point BVPs for Third-Order p ...

https://www.researchgate.net/.../46260886_Multiple_Positive_...

ResearchGate

This paper is concerned with the existence of multiple positive solutions for the third-order p-Laplacian dynamic equation (ϕp(uΔ∇(t)))∇+a(t)f(t,u(t),uΔ(t))=0,t∈[0 ...

Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales

Advances in Difference Equations (Impact Factor: 0.64). 01/2009; 2009(2). DOI: 10.1155/2009/262857

Source: OAI

ABSTRACT

This paper is concerned with the existence of multiple positive solutions for the third-order p-Laplacian dynamic equation (ϕp(uΔ∇(t)))∇+a(t)f(t,u(t),uΔ(t))=0,t∈[0,T]핋 with the multipoint boundary conditions uΔ(0)=uΔ∇(0)=0,u(T)+B0(∑i=1m−2biuΔ(ξi))=0, where ϕp(u)=|u|p−2u with p>1. Using the fixed point theorem due to Avery and Peterson, we establish the existence criteria of at least three positive solutions to the problem. As an application, an example is given to illustrate the result. The interesting points are that not only do we consider third-order p-Laplacian dynamic equation but also the nonlinear term f is involved with the first-order delta derivative of the unknown function.

Multiple Positive Solutions of m-Point BVPs for Third-Order p-Laplacian Dynamic Equations on Time Scales (PDF Download Available). Available from: https://www.researchgate.net/publication/46260886_Multiple_Positive_Solutions_of_m-Point_BVPs_for_Third-Order_p-Laplacian_Dynamic_Equations_on_Time_Scales [accessed Mar 30, 2016].

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phymath999

Wednesday, March 30, 2016

the existence of multiple positive solutions for the third-order p-Laplacian dynamic equation (ϕp(uΔ∇(t)))∇+a(t)f(t,u(t),uΔ(t))=0,t∈[0,T]핋 with the multipoint boundary conditions uΔ(0)=uΔ∇(0)=0,u(T)+B0(∑i=1m−2biuΔ(ξi))=0, where ϕp(u)=|u|p−2u with p>1.