Existence of periodic solution for a class of beam equation via variational methods

Alves, Claudianor O.; Araújo, Bruno S. V.; Nóbrega, Alânnio B.

doi:10.1007/s00605-021-01583-z

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…Due to the widespread application of differential equations in practice, in recent decades, many theories and methods of nonlinear analysis, such as the spaces theories [26][27][28][29][30][31], smoothness theories [32][33][34][35], operator theories [36][37][38], fixed-point theorems [18,21,24,25,[39][40][41], subsuper solution methods [17,[42][43][44][45], monotone iterative techniques [12,[46][47][48][49][50][51][52][53] and the variational method [54][55][56][57][58], have been developed to study various differential equations. For example, by adopting the fixed point theorem of the mixed monotone operator, Zhou et.…”

Section: Introductionmentioning

confidence: 99%

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

et al. 2023

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In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of positive solutions for the equation including singular and nonsingular cases are established. The asymptotic behavior of the solution is also derived, which falls in between two known curves. The interesting points of this paper are that the nonlinearity of the equation may be singular in time and space variables and the corresponding operator can have a singular kernel.

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Section: Introductionmentioning

confidence: 99%

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

et al. 2023

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Periodic Solutions for a Class of Semilinear Euler–Bernoulli Beam Equations with Variable Coefficients

Wei

2023

J Dyn Diff Equat

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Solvability of fractional differential system with parameters and singular nonlinear terms

Wang,

Guo,

et al. 2024

MATH

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<p>In this article, we consider the parametric high-order fractional system with integral boundary value conditions involving derivatives of order $ p $-$ q $. With the aid of the fixed-point theorem, an exact interval from the existence to the solution of the system will be obtained, under the condition that the nonlinearities of the system may have singularities. Finally, we provide an instance to show the practicality of the primary outcomes.</p>

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Existence of periodic solution for a class of beam equation via variational methods

Cited by 3 publications

References 12 publications

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

Periodic Solutions for a Class of Semilinear Euler–Bernoulli Beam Equations with Variable Coefficients

Solvability of fractional differential system with parameters and singular nonlinear terms

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