科研之友
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摘要
We prove that positive solutions of the two-point boundary value problem u '' (x) + lambda f(u(x)) = 0, for -1 < x < 1, u(-1) = u(1) = 0, satisfying max u = u(0) > gamma, are non-singular, provided that f(u) is predominantly negative for u is an element of (0, gamma], and superlinear for u > gamma. This result adds a solution curve without turns to whatever is known about the solution set for u(0) is an element of (0, gamma). In particular, we combine it with the well-known cases of parabola-like, or S-shaped solution curves.
- 出版日期2016-6
