Speaker: Karol Wroński

Time: 17:00-18:00 pm, Februray 16, 2023, GMT+8

Venue: Zoom Meeting ID: 849 2939 2947 Password：931323
https://us06web.zoom.us/j/84929392947?pwd=TWt0QTRaOURuYWM5K2ltQ1lvcGN3dz09

Abstract:

We study a quasilinear elliptic problem $-\text{div} (\nabla \Phi(\nabla u))+V(x)N'(u)=f(u)$ with anisotropic convex function $\Phi$ on whole $\R^n$. To prove existence of a nontrivial weak solution we use mountain pass theorem for a functional defined on anisotropic Orlicz-Sobolev space $\WLPhispace(\R^n)$. As the domain is unbounded we need to use Lions type lemma formulated for Young functions. Our assumptions broaden the class of considered functions $\Phi$ so our result generalizes earlier analogous results proved in isotropic setting.

Source: School of Mathematical Sciences