5 citations · 15 across the 10 of their papers we have counts for
10 papers
Szegő-Weinberger type inequalities for symmetric domains with holes
T. V. Anoop, Vladimir Bobkov, Pavel Drabek
Let be the first positive eigenvalue of the Neumann Laplacian in a bounded domain . It was proved by Szegő for and by Weinberger for …
Existence and multiplicity results for a class of semilinear elliptic equations
Vladimir Bobkov, Pavel Drabek, Jesus Hernandez
We study the existence and multiplicity of nonnegative solutions, as well as the behaviour of corresponding parameter-dependent branches, to the equation i…
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…
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 >…
Travelling waves in the Fisher-KPP equation with nonlinear diffusion and a non-Lipschitzian reaction term
Pavel Drabek, Peter Takac
We consider a one-dimensional reaction-diffusion equation of Fisher-Kolmogoroff-Petrovsky-Piscounoff type. We investigate the effect of the interaction between the nonlinear diffus…
The Fredholm alternative for the -Laplacian in exterior domains
Pavel Drabek, Ky Ho, Abhishek Sarkar
We investigate the Fredholm alternative for the -Laplacian in an exterior domain which is the complement of the closed unit ball in (). By employing tech…
On some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the -Laplacian on a disk
Vladimir Bobkov, Pavel Drabek
We discuss several properties of eigenvalues and eigenfunctions of the -Laplacian on a ball subject to zero Dirichlet boundary conditions. Among main results, in two dimensions,…
On the structure of the second eigenfunctions of the p-Laplacian on a ball
T. V. Anoop, P. Drabek, Sarath Sasi
In this paper, we prove that the second eigenfunctions of the -Laplacian, , are not radial on the unit ball in for any Our proof relies on the var…
Landesman-Lazer condition revisited: the influence of vanishing and oscillating nonlinearities
Pavel Drabek, Martina Langerova
In this paper we deal with semilinear problems at resonance. We present a sufficient condition for the existence of a weak solution in terms of the asymptotic properties of nonline…
New patterns of travelling waves in the generalized Fisher-Kolmogorov equation
Pavel Drabek, Peter Takac
We prove the existence and uniqueness of a family of travelling waves in a degenerate (or singular) quasilinear parabolic problem that may be regarded as a generalization of the se…