Tools

LEADER 05592cam a22004937i 4500

001 ssj0002027113;

003 WaSeSS;

005 20260712090213.0;

006 m d ;

007 cr n ;

008 170613t20182018enka sb 001 0 eng d;

010 a| 2017945524;

020 a| 9780128041178 (pbk.);

020 a| 012804117X (pbk.);

035 a| (WaSeSS)ssj0002027113;

042 a| lccopycat;

049 a| EREEa| NEHH;

050 00 a| QA372b| .C15 2018;

100 1 a| Cabada, Alberto.?| UNAUTHORIZED;

245 10 a| Maximum principles for the Hill's equationh| [electronic resource] /c| Alberto Cabada, Universidade de Santiago de Compostela, Instituto de Matemáticas, Facultade de Matemáticas, Santiago de Compostela, Galicia, Spain, José Ángel Cid, Universidade de Vigo, Facultade de Matemáticas, Ourense, Galicia, Spain, Lucía López-Somoza, Universidade de Santiago de Compostela, Instituto de Matemáticas, Facultade de Matemáticas, Santiago de Compostela, Galicia, Spain.;

300 a| xiii, 238 pages :b| illustrations ;c| 23 cm.;

504 a| Includes bibliographical references and index.;

505 00 a| Machine generated contents note:g| 1.t| Introduction --g| 1.1.t| Hill's Equation --g| 1.2.t| Stability in the Sense of Lyapunov --g| 1.3.t| Floquet's Theorem for the Hill's Equation --t| References --g| 2.t| Homogeneous Equation --g| 2.1.t| Introduction --g| 2.2.t| Sturm Comparison Theory --g| 2.3.t| Spectral Properties of Dirichlet Problem --g| 2.4.t| Spectral Properties of Mixed and Neumann Problems --g| 2.5.t| Spectral Properties of the Periodic Problem: Intervals of Stability and Instability --g| 2.6.t| Relation Between Eigenvalues of Neumann, Dirichlet, Periodic, and Antiperiodic Problems --t| References --g| 3.t| Nonhomogeneous Equation --g| 3.1.t| Introduction --g| 3.2.t| The Green's Function --g| 3.3.t| Periodic Conditions --g| 3.3.1.t| Properties of the Periodic Green's Function --g| 3.3.2.t| Optimal Conditions for the Periodic MP and AMP --g| 3.3.3.t| Explicit Criteria for the Periodic AMP and MP --g| 3.3.4.t| More on Explicit Criteria --g| 3.3.5.t| Examples --g| 3.4.t| Non-Periodic Conditions --g| 3.4.1.t| Neumann Problem --g| 3.4.2.t| Dirichlet Problem --g| 3.4.3.t| Relation Between Neumann and Dirichlet Problems --g| 3.4.4.t| Mixed Problems and their Relation with Neumann and Dirichlet Ones --g| 3.4.5.t| Order of Eigenvalues and Constant Sign of the Green's Function --g| 3.4.6.t| Relations Between Green's Functions. Comparison Principles --g| 3.4.7.t| Constant Sign for Non-Periodic Green's Functions --g| 3.4.8.t| Global Order of Eigenvalues --g| 3.4.9.t| Examples --g| 3.5.t| General Second Order Equation --g| 3.5.1.t| Periodic Problem --g| 3.5.2.t| Non-Periodic Conditions --t| References --g| 4.t| Nonlinear Equations --g| 4.1.t| Introduction --g| 4.2.t| Fixed Point Theorems and Degree Theory --g| 4.2.1.t| Leray-Schauder Degree --g| 4.2.2.t| Fixed Point Theorems --g| 4.2.3.t| Extremal Fixed Points --g| 4.2.4.t| Monotone Operators --g| 4.2.5.t| Non-increasing Operators --g| 4.2.6.t| Non-decreasing Operators --g| 4.2.7.t| Problems with Parametric Dependence --g| 4.3.t| Lower and Upper Solutions Method --g| 4.3.1.t| Well Ordered Lower and Upper Solutions --g| 4.3.2.t| Existence of Extremal Solutions --g| 4.3.3.t| Non-Well-Ordered Lower and Upper Solutions --g| 4.4.t| Monotone Iterative Techniques --g| 4.4.1.t| Well Ordered Lower and Upper Solutions --g| 4.4.2.t| Reversed Ordered Lower and Upper Solutions --t| References.;

506 a| Available only to authorized users.;

650 7 a| Hill's equation.2| fast0| (OCoLC)fst00956809;

520 a| Maximum 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.--c| Source other than the Library of Congress.;

538 a| Mode of access: World Wide Web;

650 0 a| Hill's equation.=| ^A275571;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Cid, Joséq| (José Angel)?| UNAUTHORIZED;

700 1 a| López-Somoza, Lucia.?| UNAUTHORIZED;

856 40 z| Full text available from eBooks on EBSCOhostu| https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1144607&scope=site&custid=s5822723&authtype=ip,shib;

856 40 z| Full text available from eBook - Mathematics 2018 [EBCM18]u| https://go.openathens.net/redirector/ecu.edu?url=https%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Fbook%2F9780128041178;

947 a| (OCoLC)ocn979562421;

949 a| CLICK ON WEB ADDRESSw| ASISh| JOYNER188;

949 a| CLICK ON WEB ADDRESSw| ASISh| HSL77;

949 a| CLICK ON WEB ADDRESSw| ASISh| JMUSIC60;

596 a| 1 3 4;

998 a| 5865808;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5865808-1001l| JNETm| JOYNERr| Ys| Yt| JNESSBKu| 7/18/2022x| EBOOKz| JERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5865808-2001l| HSLELECm| HSLr| Ys| Yt| HEBKu| 7/18/2022x| EBOOKz| HERESOURCE;

999 a| CLICK ON WEB ADDRESSw| ASISc| 1i| 5865808-3001l| MNETm| JMUSICr| Ys| Yt| MNESSBKu| 7/18/2022x| EBOOKz| JERESOURCE;

Maximum principles for the Hill's equation / Alberto Cabada, Universidade de Santiago de Compostela, Instituto de Matemáticas, Facultade de Matemáticas, Santiago de Compostela, Galicia, Spain, José Ángel Cid, Universidade de Vigo, Facultade de Matemáticas, Ourense, Galicia, Spain, Lucía López-Somoza, Universidade de Santiago de Compostela, Instituto de Matemáticas, Facultade de Matemáticas, Santiago de Compostela, Galicia, Spain.

Author/creator	Cabada, Alberto
Other author	Cid, José (José Angel)
Other author	López-Somoza, Lucia.
Format	Electronic
Publication Info	London ; San Diego ; Cambridge, MA ; Kidlington, Oxford : Elsevier : Academic Press, [2018]
Description	xiii, 238 pages : illustrations ; 23 cm.
Supplemental Content	Full text available from eBooks on EBSCOhost
Supplemental Content	Full text available from eBook - Mathematics 2018 [EBCM18]
Subjects	Hill's equation.

Contents	Machine generated contents note: 1. Introduction -- 1.1. Hill's Equation -- 1.2. Stability in the Sense of Lyapunov -- 1.3. Floquet's Theorem for the Hill's Equation -- References -- 2. Homogeneous Equation -- 2.1. Introduction -- 2.2. Sturm Comparison Theory -- 2.3. Spectral Properties of Dirichlet Problem -- 2.4. Spectral Properties of Mixed and Neumann Problems -- 2.5. Spectral Properties of the Periodic Problem: Intervals of Stability and Instability -- 2.6. Relation Between Eigenvalues of Neumann, Dirichlet, Periodic, and Antiperiodic Problems -- References -- 3. Nonhomogeneous Equation -- 3.1. Introduction -- 3.2. The Green's Function -- 3.3. Periodic Conditions -- 3.3.1. Properties of the Periodic Green's Function -- 3.3.2. Optimal Conditions for the Periodic MP and AMP -- 3.3.3. Explicit Criteria for the Periodic AMP and MP -- 3.3.4. More on Explicit Criteria -- 3.3.5. Examples -- 3.4. Non-Periodic Conditions -- 3.4.1. Neumann Problem -- 3.4.2. Dirichlet Problem -- 3.4.3. Relation Between Neumann and Dirichlet Problems -- 3.4.4. Mixed Problems and their Relation with Neumann and Dirichlet Ones -- 3.4.5. Order of Eigenvalues and Constant Sign of the Green's Function -- 3.4.6. Relations Between Green's Functions. Comparison Principles -- 3.4.7. Constant Sign for Non-Periodic Green's Functions -- 3.4.8. Global Order of Eigenvalues -- 3.4.9. Examples -- 3.5. General Second Order Equation -- 3.5.1. Periodic Problem -- 3.5.2. Non-Periodic Conditions -- References -- 4. Nonlinear Equations -- 4.1. Introduction -- 4.2. Fixed Point Theorems and Degree Theory -- 4.2.1. Leray-Schauder Degree -- 4.2.2. Fixed Point Theorems -- 4.2.3. Extremal Fixed Points -- 4.2.4. Monotone Operators -- 4.2.5. Non-increasing Operators -- 4.2.6. Non-decreasing Operators -- 4.2.7. Problems with Parametric Dependence -- 4.3. Lower and Upper Solutions Method -- 4.3.1. Well Ordered Lower and Upper Solutions -- 4.3.2. Existence of Extremal Solutions -- 4.3.3. Non-Well-Ordered Lower and Upper Solutions -- 4.4. Monotone Iterative Techniques -- 4.4.1. Well Ordered Lower and Upper Solutions -- 4.4.2. Reversed Ordered Lower and Upper Solutions -- References.
Abstract	Maximum 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.-- Source other than the Library of Congress.
Bibliography note	Includes bibliographical references and index.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2017945524
ISBN	9780128041178 (pbk.)
ISBN	012804117X (pbk.)

Availability

Library	Location	Call Number	Status	Item Actions
	Electronic Resources	Online Content Full text available from eBooks on EBSCOhost Full text available from eBook - Mathematics 2018 [EBCM18]	✔ Available

Click here for more information about this title

Availability