From the introduction: The authors consider a higher-order semilinear elliptic equation of the form \[ L[u]\equiv \mu\Delta^m u- a\Delta^k u= f(x,u), \quad x\equiv (x_1,x_2,\dots, x_n)\in \Omega, \] subject to the boundary conditions \[ u\bigl|_{\partial\Omega}= g_0(x), \qquad \Delta^iu\bigl|_{\partial\Omega}= g_i(x), \quad i=1,2,\dots, m-1, \] where \(\mu\) is a small positive parameter, \(\Omega\subset\mathbb{R}^n\) a bounded region with smooth boundary \(\partial\Omega\), \(m,k\) are integers, \(m> k\geq 1\), \(m+k\) is odd, \(\alpha> 0\), \(f\) is a sufficiently smooth function, and the \(g_i\) are also sufficiently smooth functions in \(\overline{\Omega}\). Using a comparison theorem, the uniform validity of the asymptotic solution is proved.