Magnus, Robert; Moschetta, Olivier Non-degeneracy of perturbed solutions of semilinear partial differential equations. (English) Zbl 1191.35132 Ann. Acad. Sci. Fenn., Math. 35, No. 1, 75-86 (2010). Summary: The equation \(-\Delta u+F(V(\varepsilon x),u)=0\) is considered in \(\mathbb R^n\). For small \(\varepsilon>0\) it is shown to possess, under appropriate conditions, a non-degenerate solution \(u_\varepsilon\) in \(H^2(\mathbb R^n)\). MSC: 35J61 Semilinear elliptic equations 35J70 Degenerate elliptic equations 47N20 Applications of operator theory to differential and integral equations 35B20 Perturbations in context of PDEs Keywords:non-degeneracy; perturbed solution; semilinear PDE PDFBibTeX XMLCite \textit{R. Magnus} and \textit{O. Moschetta}, Ann. Acad. Sci. Fenn., Math. 35, No. 1, 75--86 (2010; Zbl 1191.35132) Full Text: DOI