We study the Neumann boundary value problem for the second order ODE (Formula presented.),t∈[0,T],where (Formula presented.) is a bounded function of constant sign, (Formula presented.) are the positive/negative part of a sign-changing weight a(t) and μ>0 is a real parameter. Depending on the sign of (Formula presented.) at infinity, we find existence/multiplicity of solutions for μ in a “small” interval near the value (Formula presented.).The proof exploits a change of variables, transforming the sign-indefinite Eq. (1) into a forced perturbation of an autonomous planar system, and a shooting argument. Nonexistence results for (Formula presented.) and (Formula presented.) are given, as well.

Boscaggin, A., Garrione, M. (2016). Multiple Solutions to Neumann Problems with Indefinite Weight and Bounded Nonlinearities. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 28(1), 167-187 [10.1007/s10884-015-9430-5].

Multiple Solutions to Neumann Problems with Indefinite Weight and Bounded Nonlinearities

GARRIONE, MAURIZIO
Ultimo
2016

Abstract

We study the Neumann boundary value problem for the second order ODE (Formula presented.),t∈[0,T],where (Formula presented.) is a bounded function of constant sign, (Formula presented.) are the positive/negative part of a sign-changing weight a(t) and μ>0 is a real parameter. Depending on the sign of (Formula presented.) at infinity, we find existence/multiplicity of solutions for μ in a “small” interval near the value (Formula presented.).The proof exploits a change of variables, transforming the sign-indefinite Eq. (1) into a forced perturbation of an autonomous planar system, and a shooting argument. Nonexistence results for (Formula presented.) and (Formula presented.) are given, as well.
Articolo in rivista - Articolo scientifico
Bounded nonlinearities; Indefinite weight; Neumann problem; Shooting method;
Bounded nonlinearities; Indefinite weight; Neumann problem; Shooting method; Analysis
English
167
187
21
Boscaggin, A., Garrione, M. (2016). Multiple Solutions to Neumann Problems with Indefinite Weight and Bounded Nonlinearities. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 28(1), 167-187 [10.1007/s10884-015-9430-5].
Boscaggin, A; Garrione, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/146642
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