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1
Content available Existence of positive radial solutions to a p-Laplacian Kirchhoff type problem on the exterior of a ball
Graef John R., Hebboul Doudja, Moussaoui Toufik
Opuscula Mathematica
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2023
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Vol. 43, no. 1
47--66
EN
In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the p-Laplacian [formula] where λ > 0 is a parameter, Ωe = {x ∈ RN : |x| > r0}, r0 > 0, N > p > 1, Δp is the p-Laplacian operator, and f ∈ C([r0,+∞) × [0,+∞) ,R) is a non-decreasing function with respect to its second variable. By using the Mountain Pass Theorem, they prove the existence of positive radial solutions for small values of λ.
2
Content available Kneser-type oscillation criteria for second-order half-linear advanced difference equations
Indrajith N., Graef John R., Thandapani E.
Opuscula Mathematica
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2022
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Vol. 42, no. 1
55--64
EN
The authors present Kneser-type oscillation criteria for a class of advanced type second-order difference equations. The results obtained are new and they improve and complement known results in the literature. Two examples are provided to illustrate the importance of the main results.
3
Content available Extremal solutions to a coupled system of nonlinear fractional differential equations with ψ–Caputo fractional derivatives
Derbazi Choukri, Baitiche Zidane, Benchohra Mouffak, Graef John R.
Journal of Mathematics and Applications
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2021
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Vol. 44
19--34
EN
Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the ψ–Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.
4
Content available On the asymptotic behavior of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
Graef John R., Grace Said R., Tune Ercan
Opuscula Mathematica
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2020
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Vol. 40, no. 2
227--239
EN
This paper is concerned with the asymptotic behavior of the nonoscillatory solutions of the forced fractional differential equation with positive and negative terms of the form [formula] where t ≥ c ≥ α ∈(0, 1), η ≥ 1 is the ratio of positive odd integers, and [formula] denotes the Caputo fractional derivative of y of order α. The cases [formula] are considered. The approach taken here can be applied to other related fractional differential equations. Examples are provided to illustrate the relevance of the results obtained.
5
Content available Oscillatory behavior of even-order nonlinear differential equations with a sublinear neutral term
Graef John R., Grace Said R., Tunc Ercan
Opuscula Mathematica
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2019
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Vol. 39, no. 1
39--47
EN
The authors present a new technique for the linearization of even-order nonlinear differential equations with a sublinear neutral term. They establish some new oscillation criteria via comparison with higher-order linear delay differential inequalities as well as with first-order linear delay differential equations whose oscillatory characters are known. Examples are provided to illustrate the theorems.
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