The barrier strip technique for a boundary value problem with p-Laplacian

Abstract

We study the solvability of the boundary value problem $$ (phi_p(x'))'=f(t,x,x'),quad x(0)=A,;x'(1)=B, $$ where $phi_p(s)=s|s|^{p-2}$, using the barrier strip type arguments. We establish the existence of $C^2[0,1]$-solutions, restricting our considerations to $pin(1,2]$. The existence of positive monotone solutions is also considered.

Keywords

• Boundary value problem
• second order differential equation
• p-Laplacian, sign condition