In the present note we establish an almost-optimal solvability result for Kirchhoff-type problems of the following form{--M (||Delta u||L2(Omega)) = u= fz(x,u) in f(x, u) in Omega,u >=, L2(omega) u > 0, in Omega u = 0 on partial derivative Omega.partial differential n. where f has sublinear growth and M is a non-decreasing map with M(0) >= 0. Our approach is purely variational, and the result we obtain is resemblant to the one established by Brezis and Oswald (Nonlinear Anal., 1986) for sublinear elliptic equations.
Biagi, S., Vecchi, E. (2024). ON A BREZIS-OSWALD-TYPE RESULT FOR DEGENERATE KIRCHHOFF PROBLEMS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 44(3), 702-717 [10.3934/dcds.2023122].
ON A BREZIS-OSWALD-TYPE RESULT FOR DEGENERATE KIRCHHOFF PROBLEMS
Vecchi, E
2024
Abstract
In the present note we establish an almost-optimal solvability result for Kirchhoff-type problems of the following form{--M (||Delta u||L2(Omega)) = u= fz(x,u) in f(x, u) in Omega,u >=, L2(omega) u > 0, in Omega u = 0 on partial derivative Omega.partial differential n. where f has sublinear growth and M is a non-decreasing map with M(0) >= 0. Our approach is purely variational, and the result we obtain is resemblant to the one established by Brezis and Oswald (Nonlinear Anal., 1986) for sublinear elliptic equations.| File | Dimensione | Formato | |
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