Results 21 to 30 of about 317,930 (233)
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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Almost Periodic Solutions of First-Order Ordinary Differential Equations
Mathematics, 2018 Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found.
Seifedine Kadry +3 more
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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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Causal difference equations with upper and lower solutions in the reverse order
Advances in Difference Equations, 2019 This paper is devoted to studying the existence conditions for difference equations involving causal operators in the presence of upper and lower solutions in the reverse order. To this end, we prove some new comparison theorems and develop the upper and
Wen-Li Wang, Jing-Feng Tian
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The upper–lower solution method for the coupled system of first order nonlinear PDEs
Journal of Mathematical Analysis and Applications, 2013 Abstract This paper is concerned with a coupled system of first order nonlinear partial differential equations. This system is, but not limited in, the extended case of the general blood–tissue exchange model (BTEX). We use the solutions of a coupled system of first order ordinary differential equations to construct a pair of ordered lower and upper ...
Guo-Chin Jau, Yu-Hsien Chang
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On positive solutions of the Dirichlet problem involving the extrinsic mean curvature operator
Electronic Journal of Qualitative Theory of Differential Equations, 2016 In this paper, we are concerned with necessary conditions for the existence of positive solutions of the Dirichlet problem for the prescribed mean curvature equation in Minkowski space \begin{equation*} \begin{aligned} -\text{div}\left(\frac {\nabla u}{\
Ruyun Ma, Tianlan Chen, Hongliang Gao
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Malaya Journal of Matematik, 2018 Our aim is to develop the method of upper lower solutions and apply it to prove existence and uniqueness ofsolution of periodic boundary value problems for a system of fractional differential equations involving a Riemann- Liouville fractional derivatives.
null D.B. Dhaigude +2 more
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Fractal and Fractional, 2022 The aim of this research work is to derive some appropriate results for extremal solutions to a class of generalized Caputo-type nonlinear fractional differential equations (FDEs) under nonlinear boundary conditions (NBCs).
Choukri Derbazi +5 more
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Well-Ordered and Non-Well-Ordered Lower and Upper Solutions for Periodic Planar Systems
Advanced Nonlinear Studies, 2021 The aim of this paper is to extend the theory of lower and upper solutions to the periodic problem associated with planar systems of differential equations.
Fonda Alessandro +2 more
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The method of upper, lower solutions and monotone iterative scheme for higher order hyperbolic partial differential equations [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1989 AbstractUniformly monotone convergent iterative methods for obtaining multiple solutions of (n + m)th order hyperbolic partial differential equations together with initial conditions are discussed. Appropriate partial differential inequalities which connect upper and lower solutions, and variation of parameters formula is developed.
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