Asymptotic expansion of the variational eigencurve for two-parameter simple pendulum-type equations Original Research Article

We consider the nonlinear two-parameter simple pendulum-type equation View the MathML source where p>1 is a constant and μ,λ>0 are parameters. For a given μ>0, there exists a solution triple View the MathML source, which is obtained by a variational method, such that ||uμ||∞→0 as μ→∞. We establish the precise asymptotic formula for the variational eigencurve λ(μ) as μ→∞, whose growth order is sublinear.