TY - JOUR A2 - Kenmochi, Nobuyuki AU - Hsu, Tsing-San PY - 2011 DA - 2011/06/28 TI - Multiple Positive Solutions for Semilinear Elliptic Equations with Sign-Changing Weight Functions in 𝑁 SP - 864296 VL - 2011 AB - Existence and multiplicity of positive solutions for the followingsemilinear elliptic equation: Δu+u=a(x)|u|p2u+λb(x)|u|q2u in N, uH1(N), are established, where λ>0,1<q<2<p<2*  (2*=2N/(N2) if N3,2*= if N=1,2), a, b satisfy suitable conditions, and b maybe changes sign in N. The study is based on the extraction of the Palais-Smale sequences in the Nehari manifold. SN - 1085-3375 UR - https://doi.org/10.1155/2011/864296 DO - 10.1155/2011/864296 JF - Abstract and Applied Analysis PB - Hindawi Publishing Corporation KW - ER -