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Title: Nonlinear periodic problems superlinear at $+infty$ and sublinear at. $-infty$
Author: Aizicovici, S.
Papageorgiou, N. S.
Staicu, V.
Keywords: Asymmetric reaction
Nonhomogeneous differential opertator
Critical groups
Homotopy equivalent
mountain pass theorem
Issue Date: 2013
Publisher: American Romanian Academy
Abstract: We consider a nonlinear periodic problem driven by a nonlinear, nonhomogeneous differential operator with a reaction which exhibits an asymmetric growth at $+\infty$ and at $-\infty$. It is $\left( p-1\right) -$superlinear near $+\infty$ and $\left( p-1\right) -$ sublinear near $-\infty$. A particular case of our problem is that of periodic equations with the scalar $p-$ Laplacian and an asymmetric nonlinearity. Using variational methods and Morse theory, we prove the existence of at least three nontrivial solutions.
Peer review: yes
ISSN: 2182-567X
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Appears in Collections:CIDMA - Artigos
FAAG - Artigos

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