| 1 Preliminaries |
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| Sobolev spaces and embedding theorems |
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| Critical point |
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| Cone and partial order |
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| Brouwer Degree |
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| Compact map and Leray-Schauder Degree |
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| Fredholm operators |
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| Fixed point index |
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| Banach's Contract Theorem, Implicit Functions Theorem |
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| Krein-Rutman theorem |
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| Bifurcation theory |
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| Rearrangements of sets and functions |
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| Genus and Category |
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| Maximum principles and symmetry of solution |
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| Comparison theorems |
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| 2 Cone and Partial Order Methods |
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| Increasing operators |
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| Decreasing operators |
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| Mixed monotone operators |
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| Applications of mixed monotone operators |
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| Further results on cones and partial order methods |
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| 3 Minimax Methods |
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| Mountain Pass Theorem and Minimax Principle |
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| Linking Methods |
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| Local linking Methods |
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| 4 Bifurcation and Critical Point |
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| Introduction |
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| Main results with parameter |
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| Equations without the parameter |
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| 5 Solutions of a Class of Monge-Ampère Equations |
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| Moving plane argument |
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| Existence and non-existence results |
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| Bifurcation and the equation with a parameter |
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| Appendix |
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| 6 Topological Methods and Applications |
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| Superlinear system of integral equations and applications |
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| Existence of positive solutions for a semilinear elliptic system |
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| 7 Dancer-Fučik Spectrum |
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| The spectrum of a self-adjoint operator |
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| Dancer-Fučik Spectrum on bounded domains |
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| Dancer-Fučik point spectrum on RN |
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| Dancer-Fučik spectrum and asymptotically linear elliptic problems |
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| 8 Sign-changing Solutions |
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| Sign-changing solutions for superlinear Dirichlet problems |
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| Sign-changing solutions for jumping nonlinear problems |
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| 9 Extension of Brezis-Nirenberg's Results and Quasilinear Problems |
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| W01,p(Ω) versus C01(Ω̄) local minimizers |
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| Multiplicity results for the quasilinear problems |
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| Uniqueness results |
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| 10 Nonlocal Kirchhoff Elliptic Problems |
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| Yang index and critical groups to nonlocal problems |
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| Variational methods and invariant sets of descent flow |
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| Uniqueness of solution for a class of Kirchhoff-type equations |
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| 11 Free Boundary Problems, System of equations for Bose-Einstein Condensate and Competing Species |
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| Competing system with many species |
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| Optimal partition problems |
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| Schrödinger systems from Bose-Einstein condensate |
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| Bibliography |
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| 1 Preliminaries |
|
| Sobolev spaces and embedding theorems |
|
| Critical point |
|
| Cone and partial order |
|
| Brouwer Degree |
|
| Compact map and Leray-Schauder Degree |
|
電子ブック
Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes [e-books]