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Non-degeneracy of perturbed solutions of semilinear partial differential equations. (English) Zbl 1191.35132

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
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