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Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems

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Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 13 Issue 3

Abstract

Uniqueness implies existence results are obtained for solutions of the fourth order ordinary differential equation, 𝑦(4) = 𝑓(𝑥, 𝑦, 𝑦′, 𝑦″, 𝑦‴), satisfying 5-point, 4-point and 3-point nonlocal boundary conditions.

Key words and phrases:: Nonlocal boundary value problem; uniqueness; existence; ordinary differential equation
Received: 2006-02-25
Published Online: 2010-03-10
Published in Print: 2006-September

© Heldermann Verlag

Articles in the same Issue

  1. Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
  2. Curves with Two Pencils and Associated Maps to Projective Spaces
  3. The Second Obstruction Functor
  4. Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
  5. Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
  6. On the Convergence of Conjugate Trigonometric Polynomials
  7. Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
  8. New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
  9. Inversion of Ahlfors and Grunsky Inequalities
  10. On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
  11. Computing Characteristic Sets of Ordinary Radical Differential Ideals
  12. Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
  13. On Systems of Linear Functional Differential Inequalities
  14. The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
  15. Fourier Series with Small Gaps
  16. Oscillations of Higher Order Functional Differential Equations with Impulses
https://doi.org/10.1515/GMJ.2006.473
Keywords for this article
Nonlocal boundary value problem; uniqueness; existence; ordinary differential equation

Articles in the same Issue

  1. Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term
  2. Curves with Two Pencils and Associated Maps to Projective Spaces
  3. The Second Obstruction Functor
  4. Ground State Solutions of Nonlinear Stationary Schrödinger Systems with Discontinuous Nonlinearity and Variable Potential
  5. Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series
  6. On the Convergence of Conjugate Trigonometric Polynomials
  7. Existence of Solutions for Fourth Order Nonlocal Boundary Value Problems
  8. New Proof of the 𝑇(1) Theorem for Triebel–Lizorkin Spaces
  9. Inversion of Ahlfors and Grunsky Inequalities
  10. On Non-Compact Operators in Weighted Ideal and Symmetric Function Spaces
  11. Computing Characteristic Sets of Ordinary Radical Differential Ideals
  12. Approximating Common Fixed Points of Nonexpansive Mappings in Banach Spaces
  13. On Systems of Linear Functional Differential Inequalities
  14. The Dirichlet Problem for a Second Order Elliptic Equation Degenerating on the Whole Boundary When the Boundary Condition Is Satisfied in the Presence of Some Weight
  15. Fourier Series with Small Gaps
  16. Oscillations of Higher Order Functional Differential Equations with Impulses
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