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Bound Sets and Two-Point Boundary Value Problems for Second Order Differential Equations

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Published/Copyright: March 10, 2010
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Georgian Mathematical Journal
From the journal Volume 14 Issue 2

Abstract

Using Mawhin's continuation principle we obtain a general result on the existence of solutions to a boundary value problem for second order nonlinear vector ODEs. Applications are given to the existence of solutions which are contained in suitable bound sets with possibly non-smooth boundary.

Key words and phrases:: Continuation principle; coincidence degree; second order differential systems; bound sets; Floquet type boundary conditions
Received: 2007-02-28
Published Online: 2010-03-10
Published in Print: 2007-June

Ā© Heldermann Verlag

Articles in the same Issue

  1. Oscillation Criteria for Fourth Order Nonlinear Difference Equations
  2. On Existence of Nonoscillatory Solutions to Quasilinear Differential Equations
  3. On Oscillation and Nonoscillation for Differential Equations with š¯‘¯-Laplacian
  4. On Approximation of the Perturbed Inclusion
  5. The Growth Condition Guaranteeing Small Solutions for a Linear Oscillator with an Increasing Elasticity Coefficient
  6. The Exponential Stability and Instability of Differential Systems with Respect to the Linear Coppelā€“Conti Approximation. Estimation of Characteristic Exponents
  7. The Dirichlet Problem for Harmonic Functions in the Smirnov Class with Variable Exponent
  8. Slowly Varying Solutions of Functional Differential Equations with Retarded and Advanced Arguments
  9. Bounded Solutions of Some Second Order Difference Equations
  10. Singular Dirichlet Boundary Value Problem for Second Order Ode
  11. Duck Trajectories of Three-Dimensional Singularly Perturbed Systems
  12. Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance
  13. On a Three-Point Boundary Value Problem for Third Order Differential Equations with Singularities in Phase Variables
  14. Bound Sets and Two-Point Boundary Value Problems for Second Order Differential Equations
https://doi.org/10.1515/GMJ.2007.385
Keywords for this article
Continuation principle; coincidence degree; second order differential systems; bound sets; Floquet type boundary conditions

Articles in the same Issue

  1. Oscillation Criteria for Fourth Order Nonlinear Difference Equations
  2. On Existence of Nonoscillatory Solutions to Quasilinear Differential Equations
  3. On Oscillation and Nonoscillation for Differential Equations with š¯‘¯-Laplacian
  4. On Approximation of the Perturbed Inclusion
  5. The Growth Condition Guaranteeing Small Solutions for a Linear Oscillator with an Increasing Elasticity Coefficient
  6. The Exponential Stability and Instability of Differential Systems with Respect to the Linear Coppelā€“Conti Approximation. Estimation of Characteristic Exponents
  7. The Dirichlet Problem for Harmonic Functions in the Smirnov Class with Variable Exponent
  8. Slowly Varying Solutions of Functional Differential Equations with Retarded and Advanced Arguments
  9. Bounded Solutions of Some Second Order Difference Equations
  10. Singular Dirichlet Boundary Value Problem for Second Order Ode
  11. Duck Trajectories of Three-Dimensional Singularly Perturbed Systems
  12. Multiplicity of Solutions for Second Order Two-Point Boundary Value Problems with Asymptotically Asymmetric Nonlinearities at Resonance
  13. On a Three-Point Boundary Value Problem for Third Order Differential Equations with Singularities in Phase Variables
  14. Bound Sets and Two-Point Boundary Value Problems for Second Order Differential Equations
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