On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions

Khanfer, Ammar; Bougoffa, Lazhar

doi:10.3934/math.2021575

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…It is enough to prove the operator F has a unique fixed point ϑ * ∈ D with Fϑ * = ϑ * . According to (17), every such fixed point will also lie in C (4) ([a, b]) as can be directly shown by differentiating (10).…”

Section: Main Results Based On Metricsmentioning

confidence: 99%

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Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions

2023

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The objective of this paper is to investigate the existence and uniqueness of solutions to fourth order differential equations v(4) (x) + f (x, v(x)) = 0, x∈[a,b],satisfying the three-point non-homogeneous conditions v(a) = 0, v′(a) = 0, v′′(a) = 0, v′(b) −α v′(ζ ) = μ,where 0 ≤ a < ζ < b, the constants α, μ are real numbers and f : [a, b] × R → R is a continuous function. The framework for establishing the existence results is based on sharper estimates on the integral of the kernel to connect with fixed point theorems of Banach and Rus.

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Section: Main Results Based On Metricsmentioning

confidence: 99%

“…In 2021, Khanfer and Bougoffa [17] established the existence and uniqueness theorem for the nonlocal fourth order nonlinear beam differential equations with a parameter…”

Section: Introductionmentioning

confidence: 99%

Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions

2023

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Existence of Solutions to Nonlinear Fourth-Order Beam Equation

Ostaszewska

Schmeidel

Zdanowicz

2023

Qual. Theory Dyn. Syst.

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A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data

Khanfer

Bougoffa

2021

Journal of Function Spaces

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The boundary value problem of a fourth-order beam equation u 4 = λ f x , u , u ′ , u ″ , u ′ ′ ′ , 0 ≤ x ≤ 1 is investigated. We formulate a nonclassical cantilever beam problem with perturbed ends. By determining appropriate values of λ and estimates for perturbation measurements on the boundary data, we establish an existence theorem for the problem under integral boundary conditions u 0 = u ′ 0 = ∫ 0 1 p x u x d x , u ″ 1 = u ′ ′ ′ 1 = ∫ 0 1 q x u ″ x d x , where p , q ∈ L 1 0 , 1 , and f is continuous on 0 , 1 × 0 , ∞ × 0 , ∞ × − ∞ , 0 × − ∞ , 0 .

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On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions

Cited by 5 publications

References 14 publications

Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions

Existence Results for Differential Equations of Fourth Order with Non-Homogeneous Boundary Conditions

Existence of Solutions to Nonlinear Fourth-Order Beam Equation

A Cantilever Beam Problem with Small Deflections and Perturbed Boundary Data

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