Results 1 to 10 of about 1,483,911 (151)
Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψ−Caputo Fractional Boundary Value Problem [PDF]
Fractal and Fractional, 2021 The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the ψ−Caputo derivative CDa+σ;ψϱ(t)=V(t,ϱ(t)) under integral boundary conditions ϱ(a)=λIν;ψϱ(η)+δ.
Abdelatif Boutiara +3 more
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On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique
AIMS Mathematics, 2022 <abstract><p>This paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO.
Zoubida Bouazza +6 more
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Nonlinear hemivariational inequalities of second order using the method of upper-lower solutions [PDF]
Proceedings of the American Mathematical Society, 2003 Summary: We examine a nonlinear hemivariational inequality of second order. The differential operator is set-valued, nonlinear and depends on both \(x\) and its gradient \(Dx\). The same is true for the zero order term \(f\), while the right-hand side nonlinearity satisfies a one-sided Lipschitz condition. We use the method of upper and lower solutions,
Kourogenis, Nikolaos C. +1 more
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Nonlinear Analysis: Modelling and Control, 2022 In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fixed ...
Xinguang Zhang +4 more
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Upper–lower solutions for nonlinear parabolic systems and their applications
Journal of Mathematical Analysis and Applications, 2011 A method of upper and lower-solutions for nonlinear time-dependent reaction-diffusion systems of the type \[ \begin{cases} {\partial \over {\partial t}} u_i(x,t) - d_i \Delta u_i(x,t)= f_i(u_1,\dots,u_m, x) \quad \text{ for } x\in \Omega \subset \mathbb R^m \\ \alpha_i u_i(x,t) + \beta_i {\partial \over \partial n} u_i(x,t) = \psi_i(u_1,\dots,u_{i-1 ...
Abudiab, Mufid, Ahn, Inkyung, Li, Lige
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The method of upper, lower solutions and hyperbolic partial differential equations
Journal of Mathematical Analysis and Applications, 1985 The authors extend the method of sub- and super-solutions to some initial value problems for certain nonlinear hyperbolic equations. They prove existence theorems and obtain minimal solutions. \{Reviewer's remark: It seems to the reviewer that their requirements on sub- and supersolutions are very restrictive.\}
Lakshmikantham, V, Pandit, S.G
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A theorem on upper–lower solutions for nonlinear elliptic systems and its applications
Journal of Mathematical Analysis and Applications, 2008 In this article the authors extend the classical result of an upper-lower solution technique to nonlinear non-homogeneous elliptic systems without the assumption of quasi-monotonicity under nonlinear boundary conditions. The method employed is Schauder's fixed point theorem.
Li, Lige, Abudiab, Mufid, Ahn, Inkyung
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On the stability of solutions of the Lichnerowicz-York equation [PDF]
, 2013 We study the stability of solution branches for the Lichnerowicz-York equation at moment of time symmetry with constant unscaled energy density. We prove that the weak-field lower branch of solutions is stable whilst the upper branch of strong-field ...
Walsh, Darragh M
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Discrete and Continuous Dynamical Systems - B, 2019 We prove existence and uniqueness of weak and classical solutions to certain semi-linear parabolic systems with Robin boundary conditions using the coupled upper-lower solution approach. Our interest lies in cross-dependencies on the gradient parts of the reaction term, which prevents the straight-forward application of standard theorems.
Anne Mund +2 more
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Semilinear elliptic equations in thin regions with terms concentrating on oscillatory boundaries [PDF]
, 2018 In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a neighborhood of the ...
Arrieta, José M. +2 more
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