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August  2006, 15(3): 759-776. doi: 10.3934/dcds.2006.15.759

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, Italy, Italy

Received  June 2005 Revised  January 2006 Published  April 2006

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.
Keywords: p-Laplacian operator., Nonlinear boundary value problem, infinite interval, heteroclinic solutions.
Mathematics Subject Classification: Primary: 34B40; Secondary: 34B1.
Citation: Barbara Bianconi, Francesca Papalini. Non-autonomous boundary value problems on the real line. Discrete & Continuous Dynamical Systems, 2006, 15 (3) : 759-776. doi: 10.3934/dcds.2006.15.759
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