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Three positive solutions for semilinear elliptic problems involving concave and convex nonlinearities

Published online by Cambridge University Press:  30 January 2012

Tsing-San Hsu  and
Huei-li Lin
Tsing-San Hsu
Affiliation:
Department of Natural Sciences, Center for General Education, Chang Gung University, Tao-Yuan 333, Taiwan (hlin@mail.cgu.edu.tw)
Huei-li Lin
Affiliation:
Department of Natural Sciences, Center for General Education, Chang Gung University, Tao-Yuan 333, Taiwan (hlin@mail.cgu.edu.tw)
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Abstract

We study the existence and multiplicity of positive solutions for the Dirichlet problem

where λ > 0, 1 < q < 2, p = 2* = 2N/(N − 2), 0 ε Ω ⊂ ℝN, N ≥ 3, is a bounded domain with smooth boundary ∂Ω and f is a non-negative continuous function on . Assuming that f satisfies some hypothesis, we prove that the equation admits at least three positive solutions for sufficiently small λ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 1 , February 2012 , pp. 115 - 135
Copyright
Copyright © Royal Society of Edinburgh 2012

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