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Existence results for asymmetric fractional p ‐Laplacian problem
Author(s) -
Pei Ruichang,
Ma Caochuan,
Zhang Jihui
Publication year - 2017
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.201600279
Subject(s) - mathematics , fractional laplacian , class (philosophy) , nonlinear system , laplace operator , pure mathematics , inequality , variational inequality , mathematical analysis , physics , quantum mechanics , artificial intelligence , computer science
We investigated a class of quasi‐linear nonlocal problems with a right‐hand side nonlinearity which exhibits an asymmetric growth at + ∞ and − ∞ . Namely, it is linear at − ∞ and superlinear at + ∞ . However, it needs not satisfy the Ambrosetti–Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by using variational methods combined with the Moser–Trudinger inequality.