000			00376nam a2200133Ia 4500
999			_c185929 _d185929
020			_a9780817681135
040			_cCUS
082			_a515.355 _bAMB/I
100			_aAmbrosetti, Antonio.
245		3	_aAn introduction to nonlinear analysis and elliptic problem/ _cAntonio Ambrosetti, David Arcoya
260			_aBostan: _bBirkhauser, _c2011.
300			_axii, 199 p. ; _c24 cm.
440			_aProgress in nonlinear differential equations and their applications, 82.
505			_aMachine generated contents note: 1.Preliminaries -- 1.1.Sobolev Spaces -- 1.1.1.Embedding Theorems -- 1.2.Linear Elliptic Equations -- 1.2.1.Frechet Differentiability -- 1.2.2.Nemitski Operators -- 1.2.3.Dirichlet Principle -- 1.2.4.Regularity of the Solutions -- 1.2.5.The Inverse of the Laplace Operator -- 1.3.Linear Elliptic Eigenvalue Problems -- 1.3.1.Linear Compact Operators -- 1.3.2.Variational Characterization of The Eigenvalues -- 2.Some Fixed Point Theorems -- 2.1.The Banach Contraction Principle -- 2.2.Increasing Operators -- 3.Local and Global Inversion Theorems -- 3.1.The Local Inversion Theorem -- 3.2.The Implicit Function Theorem -- 3.3.The Lyapunov-Schmidt Reduction -- 3.4.The Global Inversion Theorem -- 3.5.A Global Inversion Theorem with Singularities -- 4.Leray-Schauder Topological Degree -- 4.1.The Brouwer Degree -- 4.2.The Leray-Schauder Topological Degree -- 4.2.1.Index of an Isolated Zero and Computation by Linearization -- 4.3.Continuation Theorem of Leray-Schauder -- 4.3.1.A Topological Lemma -- 4.3.2.A Theorem by Leray and Schauder -- 4.4.Other Continuation Theorems -- 5.An Outline of Critical Points -- 5.1.Definitions -- 5.2.Minima -- 5.3.The Mountain Pass Theorem -- 5.4.The Ekeland Variational Principle -- 5.5.Another Min-Max Theorem -- 5.6.Some Perturbation Results -- 6.Bifurcation Theory -- 6.1.Local Results -- 6.1.1.Bifurcation from a Simple Eigenvalue -- 6.1.2.Bifurcation from an Odd Eigenvalue -- 6.2.Bifurcation for Variational Operators -- 6.2.1.A Krasnoselskii Theorem for Variational Operators -- 6.2.2.Branching Points -- 6.3.Global Bifurcation -- 7.Elliptic Problems and Functional Analysis -- 7.1.Nonlinear Elliptic Problems -- 7.1.1.Classical Formulation -- 7.1.2.Weak Formulation -- 7.2.Sub- and Super-Solutions and Increasing Operators -- 8.Problems with A Priori Bounds -- 8.1.An Elementary Nonexistence Result -- 8.2.Existence of A Priori Bounds -- 8.3.Existence of Solutions -- 8.3.1.Using the Global Inversion Theorem.
650			_aDifferential equations, Elliptic
650			_aNonlinear functional analysis
650			_aDifferentiable dynamical systems
650			_aDifferential equations, Partial
650			_aFunctional analysis
650			_aMathematics
700			_aArcoya, David.
942			_cWB16