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On Some Properties of the Dirichlet Problem at Resonance
-
Arnold Lepin
Veröffentlicht/Copyright:
10. März 2010
Abstract
The boundary value problem at resonance
𝑥″ + 𝑥 = 𝑞 sin 𝑡 + 𝑓(𝑡,𝑥,𝑥′), 𝑥(0) = 0, 𝑥(π) = 0,
is considered, where 𝑓 : [0,π] × 𝑹2 → 𝑹 is a bounded Carathéodory function, 𝑞 is a parameter. We state the multiplicity results without assuming that 𝑓 has limits.
Received: 2006-11-17
Published Online: 2010-03-10
Published in Print: 2008-March
© Heldermann Verlag
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Artikel in diesem Heft
- Functional Equations and μ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
- The Existence of Solutions for Nonlinear Operator Equations
- A Measure Theoretical Version of the Aleksandrov Theorem
- Coincidence and Fixed Points of Contractive Type Multivalued Maps
- On the 𝐿1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
- A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
- On Automorphism Groups of ω-Trees
- Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
- Singular 2D Behaviors: Homologies
- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers
Schlagwörter für diesen Artikel
Resonance;
nonlinear boundary value problem;
multiple solutions
Artikel in diesem Heft
- Functional Equations and μ-Spherical Functions
- On the Uniqueness of Meromorphic Functions That Share Two Sets
- Convergence of the Ishikawa Iterates for Multi-Valued Mappings in Convex Metric Spaces
- The Existence of Solutions for Nonlinear Operator Equations
- A Measure Theoretical Version of the Aleksandrov Theorem
- Coincidence and Fixed Points of Contractive Type Multivalued Maps
- On the 𝐿1-Convergence of Modified Cosine Sums
- On the Approximation Properties of a Class of Convolution Type Nonlinear Singular Integral Operators
- A Metric Deformation to Obtain a Positive/Negative Gaussian Curvature on a Disk
- On Automorphism Groups of ω-Trees
- Growth and Approximation of Entire Harmonic Functions in 𝑅𝑛, 𝑛 > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Gröbner Bases for the Modules Over Noetherian Polynomial Commutative Rings
- Singular 2D Behaviors: Homologies
- Integrating Over the Inverse Image of Functions in the Besov Space
- The Fourth Order of Accuracy Decomposition Scheme for Abstract Hyperbolic Equation
- On a Generalization of Partial Isometries in Banach Spaces
- A Generalized Mandelbrot Set of Polynomials of Type 𝐸𝑑 for Bicomplex Numbers