Electron. J. Diff. Equ., Vol. 2013 (2013), No. 28, pp. 1-8.

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

Petio S. Kelevedjiev, Stepan A. Tersian

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

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Petio S. Kelevedjiev
Department of Mathematics
Technical University of Sliven
Sliven, Bulgaria
email: keleved@mailcity.com
Stepan A. Tersian
Department of Mathematical Analysis
University of Ruse, Ruse, Bulgaria
email: sterzian@uni-ru.acad.bg

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