Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 28, pp. 1-8.
Title: The barrier strip technique for a boundary value problem with p-Laplacian
Authors: Petio S. Kelevedjiev (Technical Univ. of Sliven, Bulgaria)
Stepan A. Tersian (Univ. of Ruse, Bulgaria)
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 $p\in(1,2]$. The existence of positive monotone
solutions is also considered.
Submitted June 27, 2012. Published January 28, 2013.
Math Subject Classifications: 34B15, 34B18.
Key Words: Boundary value problem; second order differential equation;
p-Laplacian, sign condition