Solutions to a nonlinear Maxwell equation with two competing nonlinearities in

B Bieganowski - arXiv preprint arXiv:2010.02000, 2020 - arxiv.org
We are interested in the nonlinear, time-harmonic Maxwell equation $$\nabla\times
(\nabla\times\mathbf {E})+ V (x)\mathbf {E}= h (x,\mathbf {E})\mbox {in}\mathbb {R}^ 3$$ with …

Generalized linking-type theorem with applications to strongly indefinite problems with sign-changing nonlinearities

F Bernini, B Bieganowski - Calculus of Variations and Partial Differential …, 2022 - Springer
We show a linking-type result which allows us to study strongly indefinite problems with sign-
changing nonlinearities. We apply the abstract theory to the singular Schrödinger equation …

Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree–Fock theory

F Bernini, B Bieganowski, S Secchi - Nonlinear Analysis, 2022 - Elsevier
We are interested in a general Choquard equation− Δ+ m 2 u− m u+ V (x) u− μ| x| u=∫ RNF
(y, u (y))| x− y| N− α dyf (x, u)− K (x)| u| q− 2 u under suitable assumptions on the bounded …

Multiplicity of critical orbits to nonlinear, strongly indefinite functionals with sign-changing nonlinear part

F Bernini, B Bieganowski, D Strzelecki - arXiv preprint arXiv:2410.13315, 2024 - arxiv.org
We show an abstract critical point theorem about existence of infinitely many critical orbits to
strongly indefinite functionals with sign-changing nonlinear part defined on a dislocation …

Elliptic problems with mixed nonlinearities and potentials singular at the origin and at the boundary of the domain

B Bieganowski, A Konysz - Journal of Fixed Point Theory and Applications, 2023 - Springer
We are interested in the following Dirichlet problem:-Δ u+ λ u-μ u| x| 2-ν u dist (x, RN\Ω) 2= f
(x, u) in Ω u= 0 on∂ Ω, on a bounded domain Ω⊂ RN with 0∈ Ω. We assume that the …