Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity. (18th July 2018) - Luo, Huxiao; Li, Shengjun; He, Wenfeng
Abstract : We consider the following fractional p-Laplacian equation:- Δ p α u + V ( x ) u p - 2 u = f ( x, u ) - Γ ( x ) u q - 2 u, x ∈ R N, whereN ≥ 2, p α ⁎ > q > p ≥ 2, α ∈ ( 0, 1 ), - Δ p α is the fractionalp -Laplacian, andΓ ∈ L ∞ ( R N ) andΓ ( x ) ≥ 0 for a.e.x ∈ R N .f has the subcritical growth but higher thanΓ ( x ) u q - 2 u ; however, the nonlinearityf ( x, u ) - Γ ( x ) u q - 2 u may change sign. IfV is coercive, we investigate the existence of ground state solutions for p-Laplacian equation.