Existence of bounded trajectories via upper and lower solutions
نویسندگان
چکیده
منابع مشابه
Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions
This paper investigates the solvability of discrete Dirichlet boundary value problems by the lower and upper solution method. Here, the second order difference equation with a nonlinear right hand side f is studied and f(t, u, v) can have a superlinear growth both in u and in v. Moreover, the growth conditions on f are one-sided. We compute a priori bounds on solutions to the discrete problem a...
متن کاملEstimation of Maximal Existence Intervals for Solutions to a Riccati Equation via an Upper-Lower Solution Method
Denote by ’ the set of all real symmetric matrices. We use to 8 ‚ 8 K L K L a b denote that is positive semidefinite (definite). For or K L M œ > ß > c d ! 0 Ð_ß > Ó 0 and \ œ P Mß 8 ‚ 8 V \ 8‚8 or ’ _ , denote by the space of all bounded and measurable a b functions from to and by the space of all with M \ P Mß T − P Mß "ß_ _ a b a b \ \ T − P Mß P Mß − P Mß w _ _ _ 8 a b a b a b \ E − V ...
متن کاملExistence of stable periodic solutions for quasilinear parabolic problems in the presence of well - ordered lower and upper - solutions ∗
We present existence and stability results for periodic solutions of quasilinear parabolic equation related to Leray-Lions’s type operators. To prove existence and localization, we use the penalty method; while for stability we use an approximation scheme.
متن کاملAlmost periodic upper and lower solutions
The method of upper and lower solutions is a classical tool in the theory of periodic differential equations of the second order. We show that this method does not have a direct extension to almost periodic equations. To do this we construct equations of this type without almost periodic solutions but having two constants as ordered upper and lower solutions. r 2003 Elsevier Science (USA). All ...
متن کاملExistence of Extreme Solutions for Fractional Order Boundary Value Problem Using Upper and Lower Solutions Method in Reverse Order
In this paper, we consider the existence of extreme solutions of the boundary value problem for a fractional order differential equation Dδu = f(t, u), t ∈ [0, T ], 0 < δ < 1, 0 < T < ∞, with a nonlinear boundary conditions g(u(0)) = u(T ). Under a lower solution α and un upper solution β with β ≤ α, we establish existence results of extreme solutions by means of the method of upper and lower s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2000
ISSN: 1078-0947
DOI: 10.3934/dcds.2000.6.575