Multiple Positive Solutions for Semilinear Elliptic Equations Involving Subcritical Nonlinearities in RN

Abstract

" In this paper, we study how the shape of the graph of a(z) affects on the number of positive solutions of $$-\\Delta\\upsilon+\u03bc b(z)\\upsilon^{p-1}+\u03bb h(z)\\upsilon^{q-1}, \\qquad\\;in\\; \\mathbb{R}^N.\\qquad (0.1)$$ We prove for large enough \u03bb,\u03bc \u203a 0, there exist at least k+1 positive solutions of the this semilinear elliptic equations where 1 \u2264 q \u2039 2 \u2039 p \u2039 2*|=2N\/(N-2) for N \u2265 3."