A Priori Estimates and Existence of Positive Solutions for a Quasilinear Elliptic Equation |
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Authors: | Dong Wei |
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Affiliation: | Hebei University of Engineering Handan, Hebei 056021, China; School of Mathematics and Computer Science, University of New England Armidale, NSW 2351, Australia wdongau{at}yahoo.com.cn |
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Abstract: | On the basis of some new Liouville theorems, under suitableconditions, a priori estimates are obtained of positive solutionsof the problem where RN (N 2) is a bounded smooth domain, p>1 and isa parameter, , q are given constants such that p1<<p*1, <q, p*=Np/(Np) if N > p and p*= when N p, and a(x) is a continuous nonnegative function. Makinguse of the LeraySchauder degree of a compact mappingand a priori estimates, the paper finds that the problem abovepossesses at least one positive solution. It also discussesthe corresponding perturbed problem, where a(x) is replacedby a(x)+, >0. The results are strikingly different from thoseobtained for the case =p1. |
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