Positive solutions of semilinear equations in cones

Author:
Henrik Egnell

Journal:
Trans. Amer. Math. Soc. **330** (1992), 191-201

MSC:
Primary 35B05; Secondary 35J65

DOI:
https://doi.org/10.1090/S0002-9947-1992-1034662-5

MathSciNet review:
1034662

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Abstract: In this paper we consider the problem of finding a positive solution of the equation in a cone , with zero boundary data. We are only interested in solutions that are regular at infinity (i.e. such that , as ). We will always assume that .

We show that the existence of a solution depends on the sign of and also on the shape of the cone .

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DOI:
https://doi.org/10.1090/S0002-9947-1992-1034662-5

Article copyright:
© Copyright 1992
American Mathematical Society