Multiplicity of positive and nodal solutions for an inhomogeneous nonlinear elliptic problem

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Abstract

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.

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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

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