LEADER 04126nam 2200397 450 001 9910583381303321 005 20230120003555.0 010 $a0-12-804126-9 035 $a(MiAaPQ)EBC5106104 035 $a(EXLCZ)994340000000208898 100 $a20171117d2018 uy 0 101 0 $aeng 135 $aurcnu|||||||| 200 10$aMaximum principles for the Hill's equation$b[Recurso electrónico] /$fAlberto Cabada, Jose Angel Cid, Lucia Lopez-Somoza 210 1$aLondon, England :$cAcademic Press,$d2018. 215 $a1 recurso electrónico (254 p.) 311 $a0-12-804117-X 320 $aIncluye referencias bibliográficas al final de cada capítulo 327 $aMachine generated contents note:$g1.$tIntroduction --$g1.1.$tHill's Equation --$g1.2.$tStability in the Sense of Lyapunov --$g1.3.$tFloquet's Theorem for the Hill's Equation --$tReferences --$g2.$tHomogeneous Equation --$g2.1.$tIntroduction --$g2.2.$tSturm Comparison Theory --$g2.3.$tSpectral Properties of Dirichlet Problem --$g2.4.$tSpectral Properties of Mixed and Neumann Problems --$g2.5.$tSpectral Properties of the Periodic Problem: Intervals of Stability and Instability --$g2.6.$tRelation Between Eigenvalues of Neumann, Dirichlet, Periodic, and Antiperiodic Problems --$tReferences --$g3.$tNonhomogeneous Equation --$g3.1.$tIntroduction --$g3.2.$tThe Green's Function --$g3.3.$tPeriodic Conditions --$g3.3.1.$tProperties of the Periodic Green's Function --$g3.3.2.$tOptimal Conditions for the Periodic MP and AMP --$g3.3.3.$tExplicit Criteria for the Periodic AMP and MP --$g3.3.4.$tMore on Explicit Criteria --$g3.3.5.$tExamples --$g3.4.$tNon-Periodic Conditions --$g3.4.1.$tNeumann Problem --$g3.4.2.$tDirichlet Problem --$g3.4.3.$tRelation Between Neumann and Dirichlet Problems --$g3.4.4.$tMixed Problems and their Relation with Neumann and Dirichlet Ones --$g3.4.5.$tOrder of Eigenvalues and Constant Sign of the Green's Function --$g3.4.6.$tRelations Between Green's Functions. Comparison Principles --$g3.4.7.$tConstant Sign for Non-Periodic Green's Functions --$g3.4.8.$tGlobal Order of Eigenvalues --$g3.4.9.$tExamples --$g3.5.$tGeneral Second Order Equation --$g3.5.1.$tPeriodic Problem --$g3.5.2.$tNon-Periodic Conditions --$tReferences --$g4.$tNonlinear Equations --$g4.1.$tIntroduction --$g4.2.$tFixed Point Theorems and Degree Theory --$g4.2.1.$tLeray-Schauder Degree --$g4.2.2.$tFixed Point Theorems --$g4.2.3.$tExtremal Fixed Points --$g4.2.4.$tMonotone Operators --$g4.2.5.$tNon-increasing Operators --$g4.2.6.$tNon-decreasing Operators --$g4.2.7.$tProblems with Parametric Dependence --$g4.3.$tLower and Upper Solutions Method --$g4.3.1.$tWell Ordered Lower and Upper Solutions --$g4.3.2.$tExistence of Extremal Solutions --$g4.3.3.$tNon-Well-Ordered Lower and Upper Solutions --$g4.4.$tMonotone Iterative Techniques --$g4.4.1.$tWell Ordered Lower and Upper Solutions --$g4.4.2.$tReversed Ordered Lower and Upper Solutions --$tReferences. 330 $aMaximum Principles for the Hill's Equation focuses on the application of these methods to nonlinear equations with singularities (e.g. Brillouin-bem focusing equation, Ermakov-Pinney,.) and for problems with parametric dependence. The authors discuss the properties of the related Green's functions coupled with different boundary value conditions. In addition, they establish the equations' relationship with the spectral theory developed for the homogeneous case, and discuss stability and constant sign solutions. Finally, reviews of present classical and recent results made by the authors and by other key authors are included.--$cSource other than the Library of Congress. 606 $aEcuación de Hill 606 $aHill's equation 615 7$aEcuación de Hill 615 0$aHill's equation. 676 $a515.352 700 $aCabada$b Alberto$0721715 702 $aCid$b Jose Angel 702 $aLopez Somoza$b Lucia 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 801 2$bUGR 906 $aBOOK 912 $a9910583381303321 996 $aMaximum principles for the Hill's equation$91914597 997 $aUNINA