Existence of Positive Global Solutions of Mixed Sublinear-Superlinear Problems

Allegretto, W. ; Huang, Y. X.

Canadian journal of mathematics, Tome 40 (1988) no. 5, pp. 1222-1242

Résumé

Consider the elliptic quasilinear problem: 1 in R n , 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.

Détail

DOI : 10.4153/CJM-1988-052-4

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