Heteroclinic connections for fully non-linear non-autonomous second-order differential equations
- Marcelli, Cristina
- Papalini, Francesca
Publication date
October 2007
DOI Publisher
Elsevier BV ISSN
0022-0396 Citation count (estimate)
17Abstract
AbstractWe investigate the solvability of the following strongly non-linear non-autonomous boundary value problem(P){(a(x(t))x′(t))′=f(t,x(t),x′(t))a.e.t∈R,x(−∞)=ν−,x(+∞)=ν+ with ν−<ν+ given constants, where a(x) is a generic continuous positive function and f is a Carathéodory non-linear function. We show that the solvability of (P) is strictly connected to a sharp relation between the behaviors of f(t,x,⋅) as |x′|→0 and f(⋅,x,x′) as |t|→+∞. Such a relation is optimal for a wide class of problems, for which we prove that (P) is not solvable when it does not hold
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