Annales Academić Scientiarum Fennicć
Mathematica
Volumen 35, 2010, 75-86

NON-DEGENERACY OF PERTURBED SOLUTIONS OF SEMILINEAR PARTIAL DIFFERENTIAL EQUATIONS

Robert Magnus and Olivier Moschetta

University of Iceland, The University Science Institute
Dunhaga 3, 107-Reykjavik, Iceland; robmag 'at' hi.is

University of Iceland, The University Science Institute
Dunhaga 3, 107-Reykjavik, Iceland; oms3 'at' hi.is

Abstract. The equation -\Delta u + F(V(e x),u) = 0 is considered in Rⁿ. For small e > 0 it is shown to possess, under appropriate conditions, a non-degenerate solution u_e in H²(Rⁿ). It is shown that the linearised operator T_e at the solution satisfies ||T_e^-1|| = O(e^-2) as e \to 0.

2000 Mathematics Subject Classification: 35J60.

Key words: Non-degeneracy, perturbed solution, semilinear PDE.

Reference to this article: R. Magnus and O. Moschetta: Non-degeneracy of perturbed solutions of semilinear partial differential equations. Ann. Acad. Sci. Fenn. Math. 35 (2010), 75-86.

Full document as PDF file

doi:10.5186/aasfm.2010.3505