6 papers · 1 filter
On the generalized Fredholm alternative for the -Laplacian with resonant subhomogeneous terms
Vladimir Bobkov
Let and let be the first eigenvalue of the -Laplacian in a bounded domain . We study the energy functional $$ E_λ(u)=\frac{1}{p}\left(\int_Ω|\nabla u|^p\…
On Pleijel-type nodal domain bounds for the -Laplacian
Vladimir Bobkov
We provide an upper estimate à la Pleijel on the asymptotic number of nodal domains for eigenfunctions corresponding to the cogenus eigenvalues of the -Laplacian…
Non-Ljusternik--Schnirelman eigenvalues of the pure -Laplacian exist
Vladimir Bobkov
An old and well-known open problem in the critical point theory asks whether, for some and some bounded domain , there exists a critical value of the -Dirichlet en…
Symmetry of fractional Neumann eigenfunctions in the ball
Vladimir Bobkov, Enea Parini
We investigate symmetry properties of the first nontrivial eigenfunctions of the fractional Laplacian , where , in an -dimensional ball with nonlocal Neuman…
Inverse iteration method for higher eigenvalues of the -Laplacian
Vladimir Bobkov, Timur Galimov
We propose a characterization of a -Laplace higher eigenvalue based on the inverse iteration method with balancing the Rayleigh quotients of the positive and negative parts of s…
A posteriori estimates for problems with monotone operators
Vladimir Bobkov, Svetlana Pastukhova
We propose a method of obtaining a posteriori estimates which does not use the duality theory and which applies to variational inequalities with monotone operators, without assumin…