کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609926 1338535 2014 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
New concentration phenomena for SU(3)SU(3) Toda system
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
New concentration phenomena for SU(3)SU(3) Toda system
چکیده انگلیسی

In this paper, we consider the following SU(3)SU(3) Toda system:equation(0.1){Δu1+2ρ2h1eu1−ρ2h2eu2=0in B1(0),Δu2+2ρ2h2eu2−ρ2h1eu1=0in B1(0),u1=u2=0on ∂B1(0), where ρ   is a positive parameter which will go to zero, h1(x)=h2(x)=h(|x|)h1(x)=h2(x)=h(|x|) is a positive smooth function, and B1(0)B1(0) is a unit ball in R2R2. In [29], the authors construct a family of solutions (u1,ρ,u2,ρ)(u1,ρ,u2,ρ) of (0.1) for h≡1h≡1, such that the solutions blow up at the origin with mass (8π,4π)(8π,4π), after some scaling with the limiting profile −Δwi=|x|αi−2ewi−Δwi=|x|αi−2ewi in R2R2, ∫R2|x|αi−2ewi<∞∫R2|x|αi−2ewi<∞, where αi=23−iαi=23−i for i=1,2i=1,2. In that paper, the authors ask whether there exist blow-up solutions of mass (8π,4π)(8π,4π), with the limiting profileΔw+2ew=0in R2,∫R2ew<∞ such that u1u1 is the sum of two bubbles and u2u2 has one bubble. In this paper, we prove that such solution exists.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 256, Issue 4, 15 February 2014, Pages 1548–1580
نویسندگان
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