Results 11 to 20 of about 327,898 (294)
Upper and Lower Solutions and Multiplicity Results
Journal of Mathematical Analysis and Applications, 2000 Using the topological degree theory, the author obtains some multiplicity results for the second-order differential equation \(x''=f(t,x,x')\), with both linear (periodic and Neumann) and nonlinear boundary conditions. Here, \(f:[a,b]\times \mathbb{R}^2 \to \mathbb{R}\) is continuous and satisfies certain growth conditions.
Rachůnková, Irena
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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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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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Upper and lower solutions satisfying the inverse inequality [PDF]
Annales Polonici Mathematici, 1997 Summary: We consider multipoint and two-point BVPs for second order ordinary differential equations with a Carathéodory right hand side. We prove the existence of solutions provided there exist upper and lower solutions of the BVP and the upper solution is less than the lower one.
Rachůnková, Irena
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Electronic Journal of Differential Equations, 2009 In this article, we study the existence of solutions to first order non-linear initial value problems within the field of "dynamic equations on time scales". We employ the method of upper and lower solutions and Schauder's fixed point theorem.
Atiya H. Zaidi
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International Journal of Differential Equations, 2011 We consider a kind of Sturm-Liouville boundary value problems. Using variational techniques combined with the methods of upper-lower solutions, the existence of at least one positive solution is established.
Li Zhang, Xiankai Huang, Weigao Ge
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Existence of solutions for Kirchhoff-type problems via the method of lower and upper solutions
Electronic Journal of Differential Equations, 2019 This article considers elliptic problems of Kirchhoff-type. We give some new definitions of lower and upper solutions for the problem and establish the method of lower and upper solutions when the upper and lower solutions are well ordered, i.e., the ...
Baoqiang Yan +2 more
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Method of upper and lower solutions for fractional differential equations
Electronic Journal of Differential Equations, 2012 In this paper, we show the existence and uniqueness of solutions for the boundary-value problems of fractional differential equations, using the upper and lower solutions method and monotone iterative algorithm.
Legang Lin, Xiping Liu, Haiqin Fang
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On lower and upper solutions without ordering on time scales [PDF]
Advances in Difference Equations, 2006 In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ordering.
Stehlík Petr
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Lower semicontinuity of attractors for non-autonomous dynamical systems [PDF]
, 2009 This paper is concerned with the lower semicontinuity of attractors for semilinear non-autonomous differential equations in Banach spaces. We require the unperturbed attractor to be given as the union of unstable manifolds of time-dependent hyperbolic
Langa, José A. +3 more
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