Again discussing about singular perturbation of general boundary value problem for higher order elliptic equation containing two-parameter (Q1058061)

The author considers the singular perturbation of a general boundary value problem for linear higher order elliptic equations containing two parameters of the form: \(L_{\epsilon,\mu}U_{\epsilon,\mu}\equiv \epsilon^{2\ell}L_{2\ell}U_{\epsilon,\mu}+\sum^{2\ell - 1}_{r=1}\mu^{\gamma}L_ rU_{\epsilon,\mu}+L_ 0U_{\epsilon,\mu}=f(x)\), where \(L_ k\) denote certain differential operators, using the method of two-variable expansions proposed firstly by \textit{F. Jiang} and \textit{R. Gao} [Kexue Tongbao 24, 1057-1061 (1979; Zbl 0423.35016)]; see also \textit{F. Jiang}, Appl. Math. Mech., Engl. Ed. 2, 505-518 (1981). Under the condition that \(L_{\epsilon,\mu}\) has a uniformly bounded inverse \(L^{-1}_{\epsilon,\mu}\) the asymptotic expression of the solution is constructed, and the remainder term is estimated. This generalizes a result of the reviewer in the first article cited above to problems containing two parameters.