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.
ON A BREZIS-OSWALD-TYPE RESULT FOR DEGENERATE KIRCHHOFF PROBLEMS / Biagi, S; Vecchi, E. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 44:3(2024), pp. 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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