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Instability of nonnegative solutions for a class of semilinear elliptic boundary value problems

โœ Scribed by C. Maya; R. Shivaji

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
171 KB
Volume
88
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

We consider the boundary value problem =O, xE~(2, where f2 is a bounded region in ~" with smooth boundary Bu(x) = cth(x)u + (1 -ct)Ou/~n where c~ E [0, 1], h : ~I2 --~ ~+ with h = 1 when ~ = 1,)~ > 0,f is a smooth function such that f"(u) > 0 for u > O, f(u) < 0 for u E (0,fl) and f(u) > 0 for u > fl for some /3 > 0. We provide a simple proof to establish that every non-trivial nonnegative solution is unstable.

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