On the solvability of a boundary value problem on the real line
1 Dipartimento di Matematica - Università di Bologna, Piazza di Porta S.Donato 5, 40126 Bologna, Italy
2 Dipartimento di Scienze Matematiche - Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy
Boundary Value Problems 2011, 2011:26 doi:10.1186/1687-2770-2011-26Published: 23 September 2011
We investigate the existence of heteroclinic solutions to a class of nonlinear differential equations
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 . 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').
Mathematical subject classification: Primary: 34B40; 34C37; Secondary: 34B15; 34L30.