کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4630050 | 1340592 | 2012 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Multiple sign-changing solutions to the Sturm-Liouville boundary value problem with resonance
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
In this paper, we study the Sturm-Liouville boundary value problem -(p(x)uâ²)â²+q(x)u=f(x,u),xâ[0,1] subject to αu(0)-βuâ²(0)=γu(1)+δuâ²(1)=0. By constructing a new Sobolev space Hα,γ1[0,1], we discuss the existence of multiple solutions, especially the existence of multiple sign-changing solutions to this problem when the nonlinear f is resonant both at 0 and â. By combining the methods of the Morse theory, the topological degree and the fixed point index, we establish a multiple solutions theorem which guarantees that the problem has at least six nontrivial solutions. If this problem has only finitely many solutions then, of these solutions, there are two positive solutions, two negative solutions and two sign-changing solutions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 219, Issue 3, 15 October 2012, Pages 1061-1072
Journal: Applied Mathematics and Computation - Volume 219, Issue 3, 15 October 2012, Pages 1061-1072
نویسندگان
Qi Zhang, Fuyi Li, Xiaoli Zhu,