کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5774250 1413552 2017 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree
ترجمه فارسی عنوان
تعدادی از راه حل های مثبت دوره ای در مورد نامحدود فوق العاده خطی از طریق درجه تقلید
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
We study the periodic boundary value problem associated with the second order nonlinear differential equationu″+cu′+(a+(t)−μa−(t))g(u)=0, where g(u) has superlinear growth at zero and at infinity, a(t) is a periodic sign-changing weight, c∈R and μ>0 is a real parameter. Our model includes (for c=0) the so-called nonlinear Hill's equation. We prove the existence of 2m−1 positive solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and μ is sufficiently large, thus giving a complete solution to a problem raised by G.J. Butler in 1976. The proof is based on Mawhin's coincidence degree defined in open (possibly unbounded) sets and applies also to Neumann boundary conditions. Our method also provides a topological approach to detect subharmonic solutions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 262, Issue 8, 15 April 2017, Pages 4255-4291
نویسندگان
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