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We consider the simple pendulum type equation with two-parameters μ, λ &gt; 0 in a ball B R . For a given μ &gt; 0, a solution triple (μ, λ(μ), u μ ) ∈ R +  2  × C 2 (B̅ R ) is obtained by a variational method, and u μ  develops a boundary layer as μ → ∞. We establish the two-term asymptotic formulas for ∥u μ ∥ ∞ , u′ μ (R) 2  and the variational eigencurve λ(μ) as μ → ∞. It is shown that the coefficients of the second terms of ∥u μ ∥ ∞ , u′ μ (R) 2  and λ(μ) depend on 1/R, the mean curvature of ∂B R . Since the second term of the maximum norm of the solution for the corresponding one parameter problems does not depend on the mean curvature of ∂B R , the results obtained here seem to be new.

Precise Asymptotic Properties of Solutions to Two-Parameter Elliptic Eigenvalue Problems in a Ball