We establish critical groups estimates for the weak solutions of −Δp u =f(x,u) in Ω and u =0 on ∂Ω via Morse index, where Ωis a bounded domain, f∈C1(Ω×R) and f(x, s) >0 for all x ∈Ω, s >0 and f(x, s) =0 for all x ∈Ω, s ≤0. The proof relies on new uniform Sobolev inequalities for approximating problems. We also prove critical groups estimates when Ω is the ball or the annulus and fis a sign changing function.
Weighted Sobolev spaces and Morse estimates for quasilinear elliptic equations
Silvia Cingolani
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2024-01-01
Abstract
We establish critical groups estimates for the weak solutions of −Δp u =f(x,u) in Ω and u =0 on ∂Ω via Morse index, where Ωis a bounded domain, f∈C1(Ω×R) and f(x, s) >0 for all x ∈Ω, s >0 and f(x, s) =0 for all x ∈Ω, s ≤0. The proof relies on new uniform Sobolev inequalities for approximating problems. We also prove critical groups estimates when Ω is the ball or the annulus and fis a sign changing function.File in questo prodotto:
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