Existence and Multiplicity of Positive Solutions to a Class of Quasilinear Elliptic Equations in ℝN. (8th March 2010) - Hsu Hsu, Tsing-San Tsing-San
Abstract : We consider the following class of quasilinear elliptic equations - h p Δ p u + V ε ( x ) | u | p - 2 u = | u | q - 2 u, u ( x ) > 0 for all x ∈ ℝ N, where h > 0, Δ p u = div ( | ∇ u | p - 2 ∇ u ), 2 ≤ p < N, p < q < p * = N p / ( N - p ) . We allow the potential V ε to be unbounded below and prove the existence and multiplicity for positive solutions.