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

Author:

Cupini Giovanni,Marcelli Cristina,Papalini Francesca

Abstract

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 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'). Mathematical subject classification: Primary: 34B40; 34C37; Secondary: 34B15; 34L30.

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory,Analysis

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