5 papers · 2 filters
On partially free boundary solutions for elliptic problems with non-Lipschitz nonlinearities
Vladimir Bobkov, Pavel Drábek, Yavdat Ilyasov
We show that the elliptic equation with a non-Lipschitz right-hand side, with and , considered on a smooth star-shaped domain su…
On the Fredholm-type theorems and sign properties of solutions for -Laplace equations with two parameters
Vladimir Bobkov, Mieko Tanaka
We consider the Dirichlet problem for the nonhomogeneous equation in a bounded domain, where , and …
Estimates on the spectral interval of validity of the anti-maximum principle
Vladimir Bobkov, Pavel Drabek, Yavdat Il'yasov
The anti-maximum principle for the homogeneous Dirichlet problem to with positive states the existence of a critical value $λ_f >…
On maximum and comparison principles for parabolic problems with the -Laplacian
Vladimir Bobkov, Peter Takac
We investigate strong and weak versions of maximum and comparison principles for a class of quasilinear parabolic equations with the -Laplacian $$ \partial_t u - Δ_p u = λ|u|^{p…
On exact Pleijel's constant for some domains
Vladimir Bobkov
We provide an explicit expression for the Pleijel constant for the planar disk and some of its sectors, as well as for -dimensional rectangles. In particular, the Pleijel consta…