TY - JOUR
T1 - Multiple Positive Solutions for Semilinear Elliptic Equations Involving Subcritical Nonlinearities in <em>R</em><sup><em>N</em></sup>
AU - Khademloo , Somayeh
AU - Mohsenhi , Rahelh
JO - Journal of Partial Differential Equations
VL - 1
SP - 74
EP - 94
PY - 2014
DA - 2014/03
SN - 27
DO - http://doi.org/10.4208/jpde.v27.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/5127.html
KW - Sobolev spaces
KW - semilinear elliptic equations
KW - critical exponent
KW - Nehari manifold
KW - Palais-Smale condition
AB -  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.