Existence and Nonexistence of Positive Solutions for Singular p-Laplacian Equation in ℝN. (15th December 2010) - Chen, Caisheng; Wang, Zhenqi; Wang, Fengping
Abstract : We study the existence and nonexistence of solutions for the singular quasilinear problem- div ( | x | - a p | ∇ u | p - 2 ∇ u ) = h ( x ) f ( u ) + λ H ( x ) g ( u ), x ∈ ℝ N, u ( x ) > 0, x ∈ ℝ N, lim | x | → ∞ u ( x ) = 0, where1 < p < N, 0 ≤ a < ( N − p ) / p andf ( u ) and g ( u ) behave likeu m andu n with0 < m ≤ p - 1 < n at the origin. We obtain the existence by the upper and lower solution method and the nonexistence by the test function method.