Existence and multiplicity of positive periodic solutions to Minkowski-curvature equations without coercivity condition

Yu, Xingchen; Lu, Shiping; Kong, Fanchao

doi:10.1016/j.jmaa.2021.125840

Cited by 5 publications

(2 citation statements)

References 13 publications

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“…where b(t) is a piecewise-constant sign-changing function. Motivated by the two works [6,22], the mathematicians paid their attention to the singular equations containing both attractive and repulsive singularities simultaneously or indefinite singularity (see [8,10,21,24,[35][36][37]47,52]). Thereinto, Hakl and Zamora [24], Godoy and Zamora [21] generalized equation (1.5) in a wider application.…”

Section: Introductionmentioning

confidence: 99%

Second-order differential equation with indefinite and repulsive singularities

Cui¹,

Xia²

2022

Preprint

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This paper concerns a second-order differential equation with indefinite and repulsive singularities. It is the first time to study differential equation containing both indefinite and repulsive singularities simultaneously. A set of sufficient conditions are obtained for the existence of positive periodic solutions. The theoretical underpinnings of this paper are the positivity of Green's function and fixed point theorem in cones. Our results improve and extend the results in previous literatures. Finally, three examples and their numerical simulations (phase diagrams and time diagrams of periodic solutions) are given to show the effectiveness of our conclusions.

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Section: Introductionmentioning

confidence: 99%

Second-order differential equation with indefinite and repulsive singularities

Cui¹,

Xia²

2022

Preprint

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“…Wang et al introduced the theory of fractional Sobolev spaces on time scales by conformable fractional derivatives on time scales in [9]. Recently, some other classical tools or techniques, such as the coincidence degree theory, the method of upper and lower solutions with monotone iterative technique and some fixed point theorems, etc., have been used to study the existence and multiplicity of solutions of differential equations and difference equations in the literature [10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Right Fractional Sobolev Space via Riemann–Liouville Derivatives on Time Scales and an Application to Fractional Boundary Value Problem on Time Scales

2022

Fractal Fract

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Using the concept of fractional derivatives of Riemann–Liouville on time scales, we first introduce right fractional Sobolev spaces and characterize them. Then, we prove the equivalence of some norms in the introduced spaces, and obtain their completeness, reflexivity, separability and some embeddings. Finally, as an application, we propose a recent method to study the existence of weak solutions of fractional boundary value problems on time scales by using variational methods and critical point theory, and, by constructing an appropriate variational setting, we obtain two existence results of the problem.

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