`In this paper we study the problem ⎧⎩⎨−Δu=f(u)u>0u=0in Ωε,in Ωε,on ∂Ωε, where Ωε=Ω∖B(P,ε), Ω⊂RN with N≥2 is a smooth bounded domain, B(P,ε) is the ball centered at P and radius ε>0, and f is a smooth nonlinearity. ``By some computations involving the Green function and degree theory, we compute the number and location of critical points of solutions for small ε>0.''
Critical points of positive solutions of nonlinear elliptic equations: multiplicity, location, and non-degeneracy / Grossi, Massimo; Luo, Peng. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - 72:2(2023), pp. 821-871. [10.1512/iumj.2023.72.9275]
Critical points of positive solutions of nonlinear elliptic equations: multiplicity, location, and non-degeneracy
Grossi, Massimo
Membro del Collaboration Group
;
2023
Abstract
`In this paper we study the problem ⎧⎩⎨−Δu=f(u)u>0u=0in Ωε,in Ωε,on ∂Ωε, where Ωε=Ω∖B(P,ε), Ω⊂RN with N≥2 is a smooth bounded domain, B(P,ε) is the ball centered at P and radius ε>0, and f is a smooth nonlinearity. ``By some computations involving the Green function and degree theory, we compute the number and location of critical points of solutions for small ε>0.''| File | Dimensione | Formato | |
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