Search results for "Nonlinear integral equations"

showing 2 items of 2 documents

Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

2012

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

Discrete mathematicsQuantitative Biology::Neurons and CognitionPicard–Lindelöf theoremApplied MathematicsFixed-point theoremFixed-point propertyKrasnoselskii fixed point theoremSchauder fixed point theoremNonlinear integral equationsMeasure of weak noncompactnessBrouwer fixed-point theoremKakutani fixed-point theoremContraction (operator theory)Nonlinear operatorsAnalysisMathematicsJournal of Differential Equations
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Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011

We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.

Non-Lipschitz nonlinearityVolterra integral equationMathematics::Numerical Analysissymbols.namesakeMathematics - Analysis of PDEs45D05 45G10 65R20 34A12Computer Science::Computational Engineering Finance and ScienceCollocation methodFOS: MathematicsOrthogonal collocationNonlinear integral equationsMathematics - Numerical AnalysisUniquenessMathematicsPhysics::Computational PhysicsCollocation methodsCollocationApplied MathematicsMathematical analysisComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Numerical Analysis (math.NA)Nontrivial solutionsIntegral equationComputer Science::Numerical AnalysisNonlinear systemComputational MathematicssymbolsLinear equationAnalysis of PDEs (math.AP)Journal of Computational and Applied Mathematics
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