Quasilinear Schrödinger equations with unbounded or decaying potentials | Zendy

Severo Uberlandio B. | Zendy; de Carvalho Gilson M. | Zendy

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Quasilinear Schrödinger equations with unbounded or decaying potentials

Author(s) -

Severo Uberlandio B.,

de Carvalho Gilson M.

Publication year - 2018

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201600028

Subject(s) - mathematics , infinity , class (philosophy) , minimax , space (punctuation) , type (biology) , order (exchange) , pure mathematics , mathematical analysis , schrödinger equation , mathematical optimization , linguistics , philosophy , ecology , finance , artificial intelligence , computer science , economics , biology

We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations:− Δ u + V ( | x | ) u − [ Δ ( u 2 ) ] u = Q ( | x | ) g ( u ) , x ∈ R N ,u ( x ) → 0as| x | → ∞ ,where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result.

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