Two-Point Boundary Value Problems
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns...
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This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Introduction - the history1IThe periodic problems25IIThe separated BVP75IIIRelation with degree theory135IVVariational methods189VMonotone iterative methods241VIParametric multiplicity problems279VIIResonance and non-resonance315VIIIPositive solutions345IXProblems with singular forces375XSingular perturbations405XIBibliographical notes425App. 1Degree theory435App. 2Variational methods438App. 3Spectral results441App. 4Inequalities452App. 5Maximum principle456App. 6Anti-maximum principle459
\ From the Publisher"...essential for researchers in this field."\ - Alberto Cabada in 2007K\ \
