A Class of p-q-Laplacian Type Equation with Potentials Eigenvalue Problem in RN. (9th December 2009) - Wu, Mingzhu; Yang, Zuodong
Abstract : The nonlinear elliptic eigenvalue problem− div ( | ∇ u | p − 2 ∇ u ) − div ( | ∇ u | q − 2 ∇ u ) + λ a ( x ) | u | p − 2 u + λ b ( x ) | u | q − 2 u = f ( x, u ), u ∈ W 1, p ∩ W 1, q ( R N ), where2 ≤ q ≤ p < N anda ( x ) ∈ L N / p ( R N ), b ( x ) ∈ L N / q ( R N ), a ( x ), b ( x ) > 0 are studied. The key ingredient is a special constrained minimization method.