The Fučík spectrum for the weighted operator on ℝ^N contains a first nontrivial curve that is Lipschitz continuous and strictly decreasing with known asymptotics, which is then used to prove multiplicity for related nonlinear equations.
Naito, An ODE approach to the multiplicity of self-similar solutions for semi-linear heat equations
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Fu\v{c}ik spectrum for the operator with rapidly increasing weight and applications
The Fučík spectrum for the weighted operator on ℝ^N contains a first nontrivial curve that is Lipschitz continuous and strictly decreasing with known asymptotics, which is then used to prove multiplicity for related nonlinear equations.