We investigate the existence of heteroclinic solutions to a class of nonlinear differential equations (a(x)Φ(x′(t)))′=f(t,x(t),x′(t)),a.e.t∈R governed by a nonlinear differential operator Φ extending the classical p-Laplacian, with right-hand side f having the critical rate of decay -1 as |t| → +∞, that is f(t,⋅,⋅)≈1/t. We prove general existence and non-existence results, as well as some simple criteria useful for right-hand side having the product structure f(t, x, x') = b(t, x)c(x, x').

On the solvability of a boundary value problem on the real line / Cupini, G.; Marcelli, Cristina; Papalini, Francesca. - In: BOUNDARY VALUE PROBLEMS. - ISSN 1687-2770. - ELETTRONICO. - 2011:26:(2011), pp. 1-17. [10.1186/1687-2770-2011-26]

On the solvability of a boundary value problem on the real line

MARCELLI, Cristina;PAPALINI, Francesca
2011-01-01

Abstract

We investigate the existence of heteroclinic solutions to a class of nonlinear differential equations (a(x)Φ(x′(t)))′=f(t,x(t),x′(t)),a.e.t∈R governed by a nonlinear differential operator Φ extending the classical p-Laplacian, with right-hand side f having the critical rate of decay -1 as |t| → +∞, that is f(t,⋅,⋅)≈1/t. We prove general existence and non-existence results, as well as some simple criteria useful for right-hand side having the product structure f(t, x, x') = b(t, x)c(x, x').
2011
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11566/48253
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