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The Existence of Solutions for Nonlinear Operator Equations
-
Marek Galewski
Published/Copyright:
March 10, 2010
Abstract
We provide the existence results for a nonlinear operator equation
ฮ*ฮฆโฒ (ฮ๐ฅ) = ๐นโฒ(๐ฅ),
in case ๐น โ ฮฆ is not necessarily convex. We introduce the dual variational method which is based on finding global minima of primal and dual action functionals on certain nonlinear subsets of their domains and on investigating relations between the minima obtained. The solution is a limit of a minimizng sequence whose existence and convergence are proved. The application for the non-convex Dirichlet problem with P.D.E. is given.
Received: 2006-06-15
Revised: 2007-03-02
Published Online: 2010-03-10
Published in Print: 2008-March
ยฉ Heldermann Verlag
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Articles in the same Issue
- Functional Equations and ฮผ-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 ๐ฟ1-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 ฯ-Trees
- Growth and Approximation of Entire Harmonic Functions in ๐ ๐, ๐ > 3
- On Some Properties of the Dirichlet Problem at Resonance
- Grรถbner 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 ๐ธ๐ for Bicomplex Numbers
