Abstract. We investigate the existence of bounded solutions on the whole real line of the following strongly non-linear non-autonomous differential equation (E) (a(x(t))x'(t))' = f(t, x(t), x'(t)) a.e. t \in R where a(x) is a generic continuous positive function, f is a Caratheodory right-hand side. We get existence results by combining the upper and lower-solutions method to fixed-point techniques. We also provide operative comparison criteria ensuring the well-ordering of pairs of upper and lower-solutions.

### Comparison results and existence of bounded solutions to strongly nonlinear second order differential equations

#### Abstract

Abstract. We investigate the existence of bounded solutions on the whole real line of the following strongly non-linear non-autonomous differential equation (E) (a(x(t))x'(t))' = f(t, x(t), x'(t)) a.e. t \in R where a(x) is a generic continuous positive function, f is a Caratheodory right-hand side. We get existence results by combining the upper and lower-solutions method to fixed-point techniques. We also provide operative comparison criteria ensuring the well-ordering of pairs of upper and lower-solutions.
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2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/52818
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