Results 261 to 270 of about 327,898 (294)
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Second Order Problems and Lower and Upper Solutions
2021This chapter is devoted to the study of second-order boundary value problems and second-order problems on unbounded domains. First, we prove existence of Caratheodory solutions between a pair of well-ordered lower and upper solutions and, moreover, we give additional conditions in order to guarantee the existence of extremal solutions.
Rubén Figueroa Sestelo +2 more
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Upper and lower bounds for solutions to the transport equation
AIChE Journal, 1966AbstractThe collocation method and a maximum principle are used to generate pointwise, improvable upper and lower bounds for solutions of the transport equation. This new method of analysis is applicable to the unsteady state transport equation with a specified velocity field as well as to other problems which have a maximum principle.
Bruce A. Finlayson, L. E. Scriven
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Invariance, Comparison, and Upper and Lower Solutions
1996This chapter establishes invariance and various inequalities for solutions of abstract integral equations with delay.
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Applied Mathematics and Computation, 2003
The paper is concerned with the perturbed Duffing equation \[ x''+cx'+g(t,x)=h(t). \tag{1} \] It is proved that a periodic solution to equation (1) is asymptotically stable if and only if it is bracketed by a lower solution \(\alpha\) and an upper solution \(\beta\) satisfying \(\alpha(t)>\beta(t)\) for every \(t\), provided that the derivative of \(g\)
NJOKU F. I., OMARI, PIERPAOLO
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The paper is concerned with the perturbed Duffing equation \[ x''+cx'+g(t,x)=h(t). \tag{1} \] It is proved that a periodic solution to equation (1) is asymptotically stable if and only if it is bracketed by a lower solution \(\alpha\) and an upper solution \(\beta\) satisfying \(\alpha(t)>\beta(t)\) for every \(t\), provided that the derivative of \(g\)
NJOKU F. I., OMARI, PIERPAOLO
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Upper and lower solution estimates in unilateral viscoelastodynamics
Acta Mechanica, 1987The variational and bounding method of hypercircle for linear, elliptic, boundary-value problems of mathematical physics [e.g. \textit{W. Velte}, Direkte Methoden der Variationsrechnung (1976; Zbl 0333.49035)], is extended in this paper to inequality, evolution problems of time- dependent structural mechanics.
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Lower and Upper Solutions of Boundary Value Problems
2003The method of lower and upper solutions, coupled with the monotone iterative technique provides an effective and flexible mechanism that offers theoretical as well as constructive existence results for nonlinear problems in a closed set which is generated by the lower and upper solutions.
Elvan Akin-Bohner +2 more
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Foliations, associated reductions and lower and upper solutions
2002In this interesting paper, the authors answer \textit{J. Mawhin}'s question [Boll. Unione Mat. Ital., VI. Ser., A 3, 229-238 (1984; Zbl 0547.34032)] in establishing the existence of a solution to the periodic boundary value problem \[ u''(t) + g(t,u(t)) = 0, \quad u(0)=u(T), \quad u'(0)=u'(T), \] for \(g\) asymptotically linear and satisfying a ...
C. De Coster, M.E. Tarallo
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An Overview of the Method of Lower and Upper Solutions for ODEs
2001The method of lower and upper solutions deals mainly with existence results for boundary value problems. In this presentation, we will restrict attention to second order ODE problems with separated boundary conditions. Although some of the ideas can be traced back to E.
C. De Coster, P. Habets
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Upper and lower matrix bounds of the solution for the discrete Lyapunov equation
IEEE Transactions on Automatic Control, 1996New, sharper, two sided matrix bounds for the solution of the discrete algebraic Lyapunov equation are derived utilizing the Rayleigh-Ritz inequality. Along with the author's 8 bounds, 16 older bounds are presented, giving a good review of the up-to-date state of the problem. The problem of ``stiffness'' of the solution is discussed.
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Methods of Lower and Upper Solutions
2014Stanisław Brzychczy, Roman R. Poznanski
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