Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media

Batista, Marcos R.; Mota, J. C. da

doi:10.1016/j.nonrwa.2020.103223

Cited by 8 publications

(2 citation statements)

References 14 publications

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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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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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“…As a method to study the characterizes of solutions, the upper and lower approach has been attracted much attention from a lot of researchers for many years, see [3,16,26,27,28] and references therein. Motivated by one of those papers, which establish the monotone methods in nonlinear elliptic and parabolic boundary value problems [27].…”

Section: Introductionmentioning

confidence: 99%

Monotone methods for semilinear parabolic and elliptic equations on graphs

Hu¹,

Lei²

2022

Preprint

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This paper is devoted to investigate the extinction and propagation properties of the solutions to the graph Laplacian parabolic problems with nonlinear reaction terms on networks. To this end, we establish the (strong) maximum principle for the parabolic and elliptic problems on networks. The stability of the solutions is studied by using the upper and lower solutions method to construct suitable iterative sequence. Moreover, we give examples as the application of this technique.

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Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions

Gou

2023

Fract Calc Appl Anal

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Monotone iterative method of upper and lower solutions applied to a multilayer combustion model in porous media

Cited by 8 publications

References 14 publications

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

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

Monotone methods for semilinear parabolic and elliptic equations on graphs

Extremal mild solutions to Hilfer evolution equations with non-instantaneous impulses and nonlocal conditions

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