Multiple positive solutions and bifurcation for an equation related to Choquard's equation
Multiple positive solutions and bifurcation for an equation related to Choquard's equation
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DOI：
10.1017/s0013091502000779
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发表时间：
2003-10-01
影响因子：
0.7
通讯作者：
Xia, HQ
中科院分区：
文献类型：
--
作者：
Küpper, T;Zhang, ZJ;Xia, HQ
本文研究了方程-Deltau + u =（integral（R3）\u（y）\（2）/\x-y\ dy）u + muf（x）的多个正解的存在性和分歧问题，其中f（x）是H-1（R-3）中的元素，f（x）大于等于0，f（x）不等价于0.我们证明了存在正的常数mu* 和mu**，使得当mu是（0，mu*）的元素时，方程至少有两个正解，当mu > mu** 时，方程没有正解.此外，我们证明了mu = mu* 是所研究的方程的分歧点。
In this paper we study the existence of multiple positive solutions and the bifurcation problem for the following equation:-Deltau + u = (integral(R3)\u(y)\(2)/\x-y\ dy) u + muf(x), x is an element of R-3,where f(x) is an element of H-1(R-3), f(x) greater than or equal to 0, f(x) not equivalent to 0. We show that there are positive constants mu* and mu** such that the above equation possesses at least two positive solutions for mu is an element of (0, mu*), and no positive solution for mu > mu**. Furthermore, we prove that mu = mu* is a bifurcation point for the equation under study.