Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators
Tetsutaro Shibata · International Journal of Mathematics and Mathematical Sciences · 1994
We consider the semilinear elliptic eigenvalue problem urn:x-wiley:01611712:media:ijmm431709:ijmm431709-math-0001 The asymptotic behavior of the variational eigenvalues μ = μn(r, α) obtained by Ljusternik‐Schnirelman theory is studied when the domain Ω0 is deformed continuously. We also consider the cases that Vol(Ωr) → 0, ∞ as r → ∞.