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Analysis and Topology in Nonlinear Differential Equations : A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday

By: de Figueiredo, Djairo G.
Contributor(s): Ó, Joao Marcos do | Tomei, Carlos.
Material type: TextTextSeries: eBooks on Demand.Progress in Nonlinear Differential Equations and Their Applications: Publisher: Dordrecht : Springer, 2014Description: 1 online resource (465 p.).ISBN: 9783319042145.Subject(s): Calculus of variations -- Congresses | Differential equations, Nonlinear -- Congresses | Mathematical Concepts -- CongressesGenre/Form: Electronic books.Additional physical formats: Print version:: Analysis and Topology in Nonlinear Differential Equations : A Tribute to Bernhard Ruf on the Occasion of his 60th BirthdayDDC classification: 515.355 LOC classification: QA370Online resources: Click here to view this ebook.
Contents:
Contents; Preface; Asymptotic Behavior of Sobolev Trace Embeddings in Expanding Domains; 1. Introduction; 2. Existence of extremal; 3. The limit problem; 4. Upper estimate for Cp(Ωε); 5. L∞ estimates for solutions of (Pε); 6. Proof of Theorem 1.2; 6.1. Proof of Proposition 6.1; 7. Proof of Theorem 1.3; 8. Appendix (Mean curvature); References; Multiplicity of Positive Solutions for an Obstacle Problem in R; 1. Introduction; 2. The modified obstacle problem; 3. First solution for (PA); 4. Second solution for (PA); 5. Proof of Theorem 1.1; Acknowledgement; References
Multiplicity Results for some Perturbed and Unperturbed "Zero Mass" Elliptic Problems in Unbounded Cylinders1. Introduction; 2. Variational framework; 3. Unperturbed case; 4. Bolle's perturbation arguments; 5. Preliminary lemmas; 6. Growth estimates and proof of Theorem 1.4; 7. Appendix; References; Basic Properties of Ultrafunctions; 1. Introduction; 1.1. Notation; 2. Λ-theory; 2.1. Non-Archimedean fields; 2.2. The Λ-limit; 2.3. Natural extensions of sets and functions; 2.4. Hyperfinite extensions ; 2.5. Qualified sets; 3. Ultrafunctions; 3.1. Definition of ultrafunctions
3.2. Delta-, Sigmaand Theta-basis3.3. Canonical extension of a function; 3.4. Ultrafunctions and distributions; 4. Operations with ultrafunctions; 4.1. Extension of operators ; 4.2. Derivative; 4.3. Fourier transform; 4.4. A trivial example of generalized solution; 5. Appendix; References; Multiple Radial Solutions at Resonance for Neumann Problems Involving the Mean Extrinsic Curvature Operator; 1. Introduction; 2. Multiplicity near resonance for semilinear elliptic problems; 3. Quasilinear problems involving the mean extrinsic curvature operator; 4. Variational framework
5. The multiplicity resultAcknowledgement; References; Equivariant Bifurcation in Geometric Variational Problems; 1. Introduction; 2. Connections on infinite-dimensional manifolds; 2.1. Banach vector bundles; 2.2. Connections on Banach vector bundles; 2.3. Connections and exponential maps on Banach manifolds; 2.4. Banach bundles of sections of a finite-dimensional vector bundle; 2.5. Affine maps; 2.6. Invariance; 3. Slices for continuous affine actions; 3.1. Local actions; 4. Equivariant bifurcation; 5. Geometric applications on CMC hypersurfaces; 5.1. Variational setup
5.2. A few technicalities5.3. Equivariant bifurcation using Morse index; 5.4. Equivariant bifurcation using representations; 5.5. Clifford tori in round and Berger spheres; 5.6. Rotationally symmetric surfaces in R3; Appendix A. Nonlinear formulation of the bifurcation result; References; W0 1,1 Solutions in Some Borderline Cases of Elliptic Equations with Degenerate Coercivity; 1. Introduction; 2. W0 1,1 (Ω) solutions; References; Remarks on p-Laplacian Problems Depending on the Gradient; 1. Introduction; 2. Preliminaries; 3. Radial solutions; 4. Existence of solutions in general domains
5. Applications
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QA370 (Browse shelf) http://uttyler.eblib.com/patron/FullRecord.aspx?p=1782143 Available EBL1782143

Contents; Preface; Asymptotic Behavior of Sobolev Trace Embeddings in Expanding Domains; 1. Introduction; 2. Existence of extremal; 3. The limit problem; 4. Upper estimate for Cp(Ωε); 5. L∞ estimates for solutions of (Pε); 6. Proof of Theorem 1.2; 6.1. Proof of Proposition 6.1; 7. Proof of Theorem 1.3; 8. Appendix (Mean curvature); References; Multiplicity of Positive Solutions for an Obstacle Problem in R; 1. Introduction; 2. The modified obstacle problem; 3. First solution for (PA); 4. Second solution for (PA); 5. Proof of Theorem 1.1; Acknowledgement; References

Multiplicity Results for some Perturbed and Unperturbed "Zero Mass" Elliptic Problems in Unbounded Cylinders1. Introduction; 2. Variational framework; 3. Unperturbed case; 4. Bolle's perturbation arguments; 5. Preliminary lemmas; 6. Growth estimates and proof of Theorem 1.4; 7. Appendix; References; Basic Properties of Ultrafunctions; 1. Introduction; 1.1. Notation; 2. Λ-theory; 2.1. Non-Archimedean fields; 2.2. The Λ-limit; 2.3. Natural extensions of sets and functions; 2.4. Hyperfinite extensions ; 2.5. Qualified sets; 3. Ultrafunctions; 3.1. Definition of ultrafunctions

3.2. Delta-, Sigmaand Theta-basis3.3. Canonical extension of a function; 3.4. Ultrafunctions and distributions; 4. Operations with ultrafunctions; 4.1. Extension of operators ; 4.2. Derivative; 4.3. Fourier transform; 4.4. A trivial example of generalized solution; 5. Appendix; References; Multiple Radial Solutions at Resonance for Neumann Problems Involving the Mean Extrinsic Curvature Operator; 1. Introduction; 2. Multiplicity near resonance for semilinear elliptic problems; 3. Quasilinear problems involving the mean extrinsic curvature operator; 4. Variational framework

5. The multiplicity resultAcknowledgement; References; Equivariant Bifurcation in Geometric Variational Problems; 1. Introduction; 2. Connections on infinite-dimensional manifolds; 2.1. Banach vector bundles; 2.2. Connections on Banach vector bundles; 2.3. Connections and exponential maps on Banach manifolds; 2.4. Banach bundles of sections of a finite-dimensional vector bundle; 2.5. Affine maps; 2.6. Invariance; 3. Slices for continuous affine actions; 3.1. Local actions; 4. Equivariant bifurcation; 5. Geometric applications on CMC hypersurfaces; 5.1. Variational setup

5.2. A few technicalities5.3. Equivariant bifurcation using Morse index; 5.4. Equivariant bifurcation using representations; 5.5. Clifford tori in round and Berger spheres; 5.6. Rotationally symmetric surfaces in R3; Appendix A. Nonlinear formulation of the bifurcation result; References; W0 1,1 Solutions in Some Borderline Cases of Elliptic Equations with Degenerate Coercivity; 1. Introduction; 2. W0 1,1 (Ω) solutions; References; Remarks on p-Laplacian Problems Depending on the Gradient; 1. Introduction; 2. Preliminaries; 3. Radial solutions; 4. Existence of solutions in general domains

5. Applications

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