Periodic solutions to superlinear indefinite planar systems: A topological degree approach

Feltrin, Guglielmo; Sampedro, Juan Carlos; Zanolin, Fabio

doi:10.1016/j.jde.2023.03.042

Cited by 1 publication

(2 citation statements)

References 41 publications

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“…Only a small number of published papers deal with the solvability and stability of implicit Hadamard fractional differential equations (see [48][49][50][51][52][53][54][55][56]). Some academic researchers have applied the theory of coincidence degree to study the solvability of integer-order nonlinear functional differential equations and have achieved fruitful results (see [57][58][59][60][61][62][63][64][65][66][67][68]). In the theory of coincidence degree, the construction of relevant operators is highly skilled, which brings difficulties to the application of this method.…”

Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

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A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

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The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings.

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Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

“…So it suffices to discuss the existence of solutions for BVP (61). In fact, let 61) is transformed into the form of (3).…”

mentioning

confidence: 99%

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

Periodic solutions to superlinear indefinite planar systems: A topological degree approach

Cited by 1 publication

References 41 publications

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

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