This article concerns the existence and non-existence of solutions to the strongly nonlinear non-autonomous boundary-value problem
with , where is a general increasing homeomorphism, with , a is a positive, continuous function and f is a Caratheodory nonlinear function. We provide sufficient conditions for the solvability which result to be optimal for a wide class of problems. In particular, we focus on the role played by the behaviors of and as related to that of and as .
Submitted September 3, 2012. Published October 4, 2012.
Math Subject Classifications: 34B40, 34C37, 34B15, 34L30.
Key Words: Boundary value problems; unbounded domains; heteroclinic solutions; nonlinear differential operators; p-Laplacian operator; Phi-Laplacian operator
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| Cristina Marcelli |
Dipartimento di Scienze Matematiche
Università Politecnica delle Marche
Via Brecce Bianche, 60131 Ancona, Italy
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