We deal with positive solutions for the Neumann boundary value problem associated with the scalar second order ODE u″ + q(t)g(u) = 0, t ϵ [0, T]; where g : [0,+∞[→ R is positive on ]0,+ ∞ [ and q(t) is an indefinite weight. Complementary to previous investigations in the case ∫T0 q(t) < 0, we provide existence results for a suitable class of weights having (small) positive mean, when g′(u) < 0 at infinity. Our proof relies on a shooting argument for a suitable equivalent planar system of the type x′ = y, y′ = h(x)y2 + q(t); with h(x) a continuous function defined on the whole real line.

Boscaggin, A., Garrione, M. (2016). Positive solutions to indefinite neumann problems when the weight has positive average. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 36(10), 5231-5244 [10.3934/dcds.2016028].

Positive solutions to indefinite neumann problems when the weight has positive average

GARRIONE, MAURIZIO
2016

Abstract

We deal with positive solutions for the Neumann boundary value problem associated with the scalar second order ODE u″ + q(t)g(u) = 0, t ϵ [0, T]; where g : [0,+∞[→ R is positive on ]0,+ ∞ [ and q(t) is an indefinite weight. Complementary to previous investigations in the case ∫T0 q(t) < 0, we provide existence results for a suitable class of weights having (small) positive mean, when g′(u) < 0 at infinity. Our proof relies on a shooting argument for a suitable equivalent planar system of the type x′ = y, y′ = h(x)y2 + q(t); with h(x) a continuous function defined on the whole real line.
Articolo in rivista - Articolo scientifico
Average condition; Indefinite weight; Neumann problem; Shooting method;
Average condition; Indefinite weight; Neumann problem; Shooting method; Discrete Mathematics and Combinatorics; Applied Mathematics; Analysis
English
5231
5244
14
Boscaggin, A., Garrione, M. (2016). Positive solutions to indefinite neumann problems when the weight has positive average. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 36(10), 5231-5244 [10.3934/dcds.2016028].
Boscaggin, A; Garrione, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/146638
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