کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
841587 908514 2011 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Resonance and rotation numbers for planar Hamiltonian systems: Multiplicity results via the Poincaré–Birkhoff theorem
چکیده انگلیسی

In the general setting of a planar first order system equation(0.1)u′=G(t,u),u∈R2, with G:[0,T]×R2→R2G:[0,T]×R2→R2, we study the relationships between some classical nonresonance conditions (including the Landesman–Lazer one) — at infinity and, in the unforced case, i.e. G(t,0)≡0G(t,0)≡0, at zero — and the rotation numbers of “large” and “small” solutions of (0.1), respectively. Such estimates are then used to establish, via the Poincaré–Birkhoff fixed point theorem, new multiplicity results for TT-periodic solutions of unforced planar Hamiltonian systems Ju′=∇uH(t,u)Ju′=∇uH(t,u) and unforced undamped scalar second order equations x″+g(t,x)=0x″+g(t,x)=0. In particular, by means of the Landesman–Lazer condition, we obtain sharp conclusions when the system is resonant at infinity.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 74, Issue 12, August 2011, Pages 4166–4185
نویسندگان
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