Multiple positive solutions of a nonlinear boundary value problem involving a sign-changing weight Original Research Article

In this paper, we study the multiplicity of positive solutions for the following elliptic equation: View the MathML source{Δu−u=0in R+N,∂u∂ν=λa(x)|u|q−2u+b(x)|u|p−2uon ∂R+N, Turn MathJax on where 10} is an upper half space in RN,λ>0RN,λ>0 and the functions aa and bb are satisfying some suitable conditions. Using the decomposition of the Nehari manifold, we prove that the equation has at least two positive solutions provided λλ is sufficiently small.