In this paper, we show that there exist λ > 2 and C > 0 such that a (x) - 1 ≥ - C e- λ | x |for all x ∈ RN, the nonlinear elliptic problem - Δ u + u = a (x) | u |p - 2u + f (x) in RNhas a solution that changes sign in RN, in addition to two positive solutions. © 2007 Elsevier Ltd. All rights reserved.
Chen, K. J. (2009). Multiplicity of positive and nodal solutions for an inhomogeneous nonlinear elliptic problem. Nonlinear Analysis, Theory, Methods and Applications, 70(1), 194–210. https://doi.org/10.1016/j.na.2007.11.046