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Existence of Positive Global Solutions of Mixed Sublinear-Superlinear Problems

Published online by Cambridge University Press:  20 November 2018

W. Allegretto  and
Y. X. Huang
W. Allegretto
Affiliation:
University of Alberta, Edmonton, Alberta
Y. X. Huang
Affiliation:
University of Alberta, Edmonton, Alberta
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Consider the elliptic quasilinear problem:

1

in Rn, n ≧ 3, where

We are interested in establishing sufficient conditions on f for the existence of positive solutions u(x) with specified behaviour at ∞. Of special interest to us are criteria which guarantee that u(x) decays at least as fast as |x|−α for some α ≧ 0, given below, in the case f(x, u, ∇u) contains terms of type

That is: f is of mixed sublinear-super linear type. Our main result is Theorem 3 below which explicitly states sufficient conditions for the existence of such solutions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 5 , 01 October 1988 , pp. 1222 - 1242
Copyright
Copyright © Canadian Mathematical Society 1988

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