Open Access Research

Multiple positive solutions of semilinear elliptic equations involving concave and convex nonlinearities in ℝN

Huei-li Lin

Author affiliations

Department of Natural Sciences in the Center for General Education, Chang Gung University, Tao-Yuan 333, Taiwan

Citation and License

Boundary Value Problems 2012, 2012:24  doi:10.1186/1687-2770-2012-24

Published: 24 February 2012

Abstract

In this article, we investigate the effect of the coefficient f(z) of the sub-critical nonlinearity. For sufficiently large λ > 0, there are at least k + 1 positive solutions of the semilinear elliptic equations

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where 1 ≤ q < 2 < p < 2* = 2N/(N - 2) for N ≥ 3.

AMS (MOS) subject classification: 35J20; 35J25; 35J65.

Keywords:
semilinear elliptic equations; concave and convex; positive solutions