کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4611191 | 1338608 | 2010 | 52 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Positive solutions of the Dirichlet problem for the prescribed mean curvature equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We discuss existence and multiplicity of positive solutions of the prescribed mean curvature problem−div(∇u/1+|∇u|2)=λf(x,u)inΩ,u=0on∂Ω, in a general bounded domain Ω⊂RNΩ⊂RN, depending on the behavior at zero or at infinity of f(x,s)f(x,s), or of its potential F(x,s)=∫0sf(x,t)dt. Our main effort here is to describe, in a way as exhaustive as possible, all configurations of the limits of F(x,s)/s2F(x,s)/s2 at zero and of F(x,s)/sF(x,s)/s at infinity, which yield the existence of one, two, three or infinitely many positive solutions. Either strong, or weak, or bounded variation solutions are considered. Our approach is variational and combines critical point theory, the lower and upper solutions method and elliptic regularization.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 249, Issue 7, 1 October 2010, Pages 1674–1725
Journal: Journal of Differential Equations - Volume 249, Issue 7, 1 October 2010, Pages 1674–1725
نویسندگان
Franco Obersnel, Pierpaolo Omari,