Positive Solutions to Indefinite Problems by Guglielmo Feltrin
This book is devoted to the study of positive solutions to indefinite problems. The monograph intelligibly provides an extensive overview of topological methods and introduces new ideas and results. Sticking to the one-dimensional setting, the author shows that compelling and substantial research can be obtained and presented in a penetrable way.In particular, the book focuses on second order nonlinear differential equations. It analyzes the Dirichlet, Neumann and periodic boundary value problems associated with the equation and provides existence, nonexistence and multiplicity results for positive solutions. The author proposes a new approach based on topological degree theory that allows him to answer some open questions and solve a conjecture about the dependence of the number of positive solutions on the nodal behaviour of the nonlinear term of the equation. The new technique developed in the book gives, as a byproduct, infinitely many subharmonic solutions and globally defined positive solutions with chaotic behaviour. Furthermore, some future directions for research, open questions and interesting, unexplored topics of investigation are proposed.
-
Choquet Integral and Monotone Sublinear Operators
-
Exploring Information Geometry
-
Lie Models for Spaces
-
Hoop Algebras
-
Mild Differentiability Conditions for Newton's Method in Banach Spaces
-
Heat Kernel on Lie Groups and Maximally Symmetric Spaces
-
Direct and Inverse Sturm-Liouville Problems
-
Algebraic Approximation: A Guide to Past and Current Solutions
-
Advances in the Theory of Varieties of Semigroups
-
Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields
-
Poncelet Porisms and Beyond
-
Stability of Vector Differential Delay Equations
-
Applications of Holomorphic Functions in Geometry
-
A Primer for a Secret Shortcut to PDEs of Mathematical Physics
-
Ulam’s Conjecture on Invariance of Measure in the Hilbert Cube
-
Functional Analysis in Asymmetric Normed Spaces
-
Topics in Uniform Approximation of Continuous Functions
-
Infinite Matrices and their Finite Sections
-
Oblique Derivative Problems for Elliptic Equations in Conical Domains
-
Approximation of Additive Convolution-Like Operators
-
Flag-transitive Steiner Designs
-
Functions of Omega-Bounded Type
-
q-Clan Geometries in Characteristic 2
-
Lifting Modules
-
Applied Pseudoanalytic Function Theory
-
Homotopy Theory of C*-Algebras
-
The Geometry of Filtering
-
Functional Identities
-
Bicomplex Holomorphic Functions
-
Module Theory, Extending Modules and Generalizations
-
Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws
-
Nonlocal Perimeter, Curvature and Minimal Surfaces for Measurable Sets
-
Geometric Analysis of Quasilinear Inequalities on Complete Manifolds
-
Special Functions and Generalized Sturm-Liouville Problems
-
Variational Source Conditions, Quadratic Inverse Problems, Sparsity Promoting Regularization
-
Global Well-posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems
-
Shafarevich-Tate Groups
-
Variational and Monotonicity Methods in Nonsmooth Analysis
-
Quaternionic Approximation
-
Newton's Method: an Updated Approach of Kantorovich's Theory
-
Introduction to Complex Theory of Differential Equations
-
Extremum Problems for Eigenvalues of Elliptic Operators
-
Artinian Modules over Group Rings
-
Exponentially Convergent Algorithms for Abstract Differential Equations
-
Geometric Qp Functions
-
Schwarz-Pick Type Inequalities
“The book gives a complete overview of indefinite problems, starting from the more classical results in the literature up to the very recent and novel onesIt has the advantage of being self-contained, with the prerequisites recalled in the appendices and the proofs throughout the book are provided in full detail.” (Andrea Tellini, Mathematical Reviews, November, 2019)
“This book would be suitable for graduate students and young researchers willing to learn more on this fashionable topic.” (Gennaro Infante, zbMATH 1426.34002, 2020)
“This book would be suitable for graduate students and young researchers willing to learn more on this fashionable topic.” (Gennaro Infante, zbMATH 1426.34002, 2020)
| SKU | Unavailable |
| ISBN 13 | 9783319942377 |
| ISBN 10 | 3319942379 |
| Title | Positive Solutions to Indefinite Problems |
| Author | Guglielmo Feltrin |
| Series | Frontiers In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Birkhauser Verlag AG |
| Year published | 2018-12-05 |
| Number of pages | 304 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |