Asymptotic expansions for bounded solutions to semilinear Fuchsian equations
The authors study solutions \(u= u(x)\) to semilinear elliptic equations of the form \[ Au= F(x, B_1u,\dots, B_ku)\quad\text{on }X^0= X\setminus\partial X,\tag{1} \] where \(X\) is a smooth compact manifold with boundary, \(\partial X\), and of dimension \(n+1\), \(A\), \(B_1,\dots, B_k\) are Fuchsian differential operators on \(X^0\). They show that bounded solutions to (1) obey complete asymptotic expansions in terms of powers and logarithms in the distance to the boundary.
scientific article; zbMATH DE number 2095726