Non-autonomous boundary value problems on the real line

Barbara Bianconi; Francesca Papalini

doi:10.3934/dcds.2006.15.759

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2006, Volume 15, Issue 3: 759-776. Doi: 10.3934/dcds.2006.15.759

This issue Previous Article Collisionless orbits of singular and nonsingular dynamical systems Next Article Existence, uniqueness of weak solutions and global attractors for a class of nonlinear 2D Kirchhoff-Boussinesq models

Non-autonomous boundary value problems on the real line

Barbara Bianconi^1, and
Francesca Papalini^1,

1.
University of Ancona, Department of Mathematical Sciences, Via Brecce Bianche, Ancona

Received: May 31, 2005

Revised: December 31, 2005

Published: August 2006

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Abstract

We study the existence of solutions for the problem $(\Phi(x'(t)))'=f(t,x(t),x'(t))$, $x(-\infty)=0, x(+\infty)=1$, where $\Phi$: IR $\to$ IR is a monotone function which generalizes the one-dimensional p-Laplacian operator. When the right-hand side of the equation has the product structure $f(t,x,x')=a(t,x)b(x,x')$, we deduce operative criteria for the existence and non-existence of solutions.

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Mathematics Subject Classification: Primary: 34B40; Secondary: 34B15.

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