Multiplicity and bifurcation of positive solutions for nonhomogeneous semilinear elliptic problems

作者：Chen Kuan Ju^*; Peng Chen Chang

来源：Journal of Differential Equations, 2007, 240(1): 58-91.

DOI：10.1016/j.jde.2007.05.023

• nonhomogeneous semilinear elliptic problems
• multiplicity
• turning-point bifurcation

In this paper we consider the following problem
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where lambda > 0 is a parameter. We assume lim vertical bar x vertical bar ->infinity f (x, u) = (f) over bar (u) uniformly on any compact subset of [0, infinity), and do not require f (x, u) >= (f) over bar (u) for all x is an element of R-N. We prove that there exists +infinity > lambda* > 0 such that (*) has exactly two positive solutions for lambda is an element of (0, lambda*), no solution for lambda > lambda*, a unique solution for lambda = lambda*, (lambda*, u *) is a turning point in C-2,C-alpha (R-N) boolean AND W-2,W-2 (R-N), and further analyses of the set of positive solutions are made.

• 出版日期2007-9-1
• 单位中国人民解放军海军大连舰艇学院