Multiplicity of solutions for a fourth-order quasilinear nonhomogeneous equation

We consider a fourth-order quasilinear nonhomogeneous equation which is equivalent to a nonhomogeneous Hamiltonian system. The purpose of this work is to prove the existence of at least two solutions for such equation when a certain parameter is small enough. Furthermore, under an additional hypothe...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 342; no. 1; pp. 277 - 297
Main Author dos Santos, E.M.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.06.2008
Elsevier
Subjects
Algebra
Commutative rings and algebras
Exact sciences and technology
Fourth-order quasilinear equation
Global analysis, analysis on manifolds
Mathematical analysis
Mathematics
Nonhomogeneous problem
Sciences and techniques of general use
Semilinear Hamiltonian system
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Nonhomogeneous problem
Semilinear Hamiltonian system
Fourth-order quasilinear equation
Mathematical analysis
Multiplicity
Positive solution
Fourth order equation
Hamiltonian system
Application
Hamiltonian
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Summary:We consider a fourth-order quasilinear nonhomogeneous equation which is equivalent to a nonhomogeneous Hamiltonian system. The purpose of this work is to prove the existence of at least two solutions for such equation when a certain parameter is small enough. Furthermore, under an additional hypothesis on positiveness of the nonhomogeneous part we prove that our solutions are positive.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2007.11.056