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 $$-\\Delta\\upsilon+μ b(z)\\upsilon^{p-1}+λ h(z)\\upsilon^{q-1}, \\qquad\\;in\\; \\mathbb{R}^N.\\qquad (0.1)$$ We prove for large enough λ,μ > 0, there exist at least k+1 positive solutions of the this semilinear elliptic equations where 1 ≤ q < 2 < p < 2*|=2N\/(N-2) for N ≥ 3."