Sign Properties of Green's Functions for a Family of Two-Point Boundary Value Problems

Eloe, Paul W.; Ridenhour, Jerry

doi:10.2307/2159880

Cited by 6 publications

(20 citation statements)

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“…Combining (2.3), (2.14) and [8,Lemma 2.4] one gets to (2.10) and the fact that the boundary value problem (1.9) does not have a non-trivial solution as per hypothesis one has…”

Section: The Sign Of the Green Function Of The Problemmentioning

confidence: 90%

“…Next, following Eloe and Ridenhour [8] let us denote by H the partial derivative of the Green function G(x, t) of the problem (1.9) with regards to the extreme b:…”

Section: The Sign Of the Green Function Of The Problemmentioning

confidence: 99%

“…We can apply recursively [8,Lemma 2.3] to the problem (2.10) with l < n − k to determine that there are l − 1 changes of sign between y (β l ) l (x) and y …”

Section: The Sign Of the Green Function Of The Problemmentioning

confidence: 99%

See 2 more Smart Citations

Solvability of a Class of N -Th Order Linear Focal Problems

Almenar

Jódar

2017

Mathematical Modelling and Analysis

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Abstract. This paper presents a recursive method which yields necessary and sufficient conditions for the existence of solutions of a class of n-th order linear focal boundary value problems in the interior of a given interval, in the form of integral inequalities. Some results on the sign of the derivatives of the Green functions of n-th order linear focal boundary value problems will also be provided.

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“…Combining (2.3), (2.14) and [8,Lemma 2.4] one gets to (2.10) and the fact that the boundary value problem (1.9) does not have a non-trivial solution as per hypothesis one has…”

Section: The Sign Of the Green Function Of The Problemmentioning

confidence: 90%

“…Next, following Eloe and Ridenhour [8] let us denote by H the partial derivative of the Green function G(x, t) of the problem (1.9) with regards to the extreme b:…”

Section: The Sign Of the Green Function Of The Problemmentioning

confidence: 99%

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Solvability of a Class of N -Th Order Linear Focal Problems

Almenar

Jódar

2017

Mathematical Modelling and Analysis

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“…The Green's function for −D α 0 + u = 0 satisfying the boundary conditions (1.2) is given by (see [3])…”

Section: Positive Solutions Of the Auxiliary Problemmentioning

confidence: 99%

“…Recently, the Green's function for (1.1), (1.2) was found in [3] which affords us the opportunity to utilize operators and an application of Krasnosel'skii's fixed point theorem . Since f might have a singularity in the function space at x = 0, we must also use regularization and sequential techniques.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions of a singular fractional boundary value problem with a fractional boundary condition

Lyons¹,

Neugebauer²

2017

OpMath

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Abstract. For α ∈ (1, 2], the singular fractional boundary value problemsatisfying the boundary conditionsRiemann-Liouville derivatives of order α, β and µ respectively, is considered. Here f satisfies a local Carathéodory condition, and f (t, x, y) may be singular at the value 0 in its space variable x. Using regularization and sequential techniques and Krasnosel'skii's fixed point theorem, it is shown this boundary value problem has a positive solution. An example is given.

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Solvability ofNth Order Linear Boundary Value Problems

Almenar

Jódar

2015

International Journal of Differential Equations

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This paper presents a method that provides necessary and sufficient conditions for the existence of solutions ofnth order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions. The recursive comparison yields sequences of bounds of extremes that converge to the exact values of the extremes of the BVP for which a solution exists.

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Sign Properties of Green's Functions for a Family of Two-Point Boundary Value Problems

Cited by 6 publications

References 0 publications

Solvability of a Class of N -Th Order Linear Focal Problems

Solvability of a Class of N -Th Order Linear Focal Problems

Positive solutions of a singular fractional boundary value problem with a fractional boundary condition

Solvability ofNth Order Linear Boundary Value Problems

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