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Titlebook: Nonlinear Analysis and its Applications to Differential Equations; M. R. Grossinho,M. Ramos,L. Sanchez Book 2001 Birkhäuser Boston 2001 BV

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An Overview of the Method of Lower and Upper Solutions for ODEsince then a multitude of variants have been introduced. The Definitions 2.1 and 3.1 we present here tend to be general enough for applications and simple enough to model the geometric intuition built into the concept.
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Variational Inequalities,Bifurcation and Applicationsf Brézis ([.], [.]), Browder ([.], [.]), Kinderlehrer and Stampacchia ([.]), Duvaut and Lions ([.]),…. It brought about important contributions to nonlinear analysis, calculus of variations, optimization theory, optimal control, and to many branches of mechanics, mathematical physics, and engineering.
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Nonlinear Analysis and its Applications to Differential Equations
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