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A quasi-linear nonlocal Venttsel' problem of Ambrosetti–Prodi type on fractal domains
2019
Discrete and Continuous Dynamical Systems. Series A
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We investigate the solvability of the Ambrosetti-Prodi problem for the p-Laplace operator ∆p with Venttsel' boundary conditions on a twodimensional open bounded set with Koch-type boundary, and on an open bounded three-dimensional cylinder with Koch-type fractal boundary. Using a priori estimates, regularity theory and a sub-supersolution method, we obtain a necessary condition for the non-existence of solutions (in the weak sense), and the existence of at least one globally bounded weak
doi:10.3934/dcds.2019184
fatcat:p5unqr7rabhijjyj2uin3namii