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Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems
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Patricia J. Y. Wong
Veröffentlicht/Copyright:
24. Februar 2010
Abstract
We consider the boundary value problem
𝑦(𝑛) (𝑡) = 𝑃(𝑡, 𝑦), 𝑡 ∈ (0, 1)
𝑦(𝑗) (𝑡𝑖) = 0, 𝑗 = 0, . . . , 𝑛𝑖 – 1, 𝑖 = 1, . . . , 𝑟,
where 𝑟 ≥ 2, 𝑛𝑖 ≥ 1 for 𝑖 = 1, . . . , 𝑟, 
and 0 = 𝑡1 < 𝑡2 < ⋯ < 𝑡𝑟 = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.
Key words and phrases.: Generalised multipoint conjugate boundary value problem; multiple solution
Received: 1998-12-14
Published Online: 2010-02-24
Published in Print: 1999-December
© 1997 Plenum Publishing Corporation
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Artikel in diesem Heft
- Limit Distribution of the Mean Square Deviation of the Gasser–Müller Nonparametric Estimate of the Regression Function
- The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary
- On the Prandtl Equation
- On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations
- Properties 𝐴 and 𝐵 of 𝑛th Order Linear Differential Equations with Deviating Argument
- Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems
- Absolute Summability Factors and Absolute Tauberian Theorems for Double Series and Sequences
Schlagwörter für diesen Artikel
Generalised multipoint conjugate boundary value problem;
multiple solution
Artikel in diesem Heft
- Limit Distribution of the Mean Square Deviation of the Gasser–Müller Nonparametric Estimate of the Regression Function
- The Three-Dimensional Problem of Statics of the Elastic Mixture Theory with Displacements Given on the Boundary
- On the Prandtl Equation
- On the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Singular Hyperbolic Equations
- Properties 𝐴 and 𝐵 of 𝑛th Order Linear Differential Equations with Deviating Argument
- Multiple Solutions of Generalized Multipoint Conjugate Boundary Value Problems
- Absolute Summability Factors and Absolute Tauberian Theorems for Double Series and Sequences
