Periodic Solutions to Second-Order Nonlinear Differential Equations in Banach Spaces
نویسندگان
چکیده
Abstract In this article, we deal with the existence of solutions for following second-order differential equation: $$\begin{aligned} \left\{ \begin{aligned}&u''(t)=f(t,u(t))+h(t)\\&u(a)-u(b)= u'(a)-u'(b)=0, \end{aligned}\right. \end{aligned}$$ u ? ( t ) = f , + h a - b 0 where $${\mathbb {B}}$$ B is a reflexive real Banach space, $$f:[a,b]\times {\mathbb {B}}\rightarrow : [ ] × ? sequentially weak–strong continuous mapping, and $$h:[a,b]\rightarrow function on {B}}.$$ . The proofs are obtained using recent generalization well-known Bolzano–Poincaré–Miranda theorem to infinite-dimensional spaces. last section, present three examples application general result.
منابع مشابه
Periodic solutions for nonlinear Volterra integrodifferential equations in Banach spaces
In this paper we examine periodic integrodifferential equations in Banach spaces. When the cone is regular, we prove two existence theorems for the extremal solutions in the order interval determined by an upper and a lower solution. Both theorems use only the order structure of the problem and no compactness condition is assumed. In the last section we ask the cone to be only normal but we imp...
متن کاملOn the Periodic Mild Solutions to Complete Higher Order Differential Equations on Banach Spaces
For the complete higher order differential equation
متن کاملGlobal solutions for second order impulsive integro-differential equations in Banach spaces
This paper regards initial value problem for second order impulsive integro-differential equations as some nonlinear vector system. By means of the Mönch′s fixed point theorem, some existence theorems of solutions of the initial value problem are established. The results are newer than all of the previous ones because of the more general form compactness-type condition and the weaker restrictio...
متن کاملPositive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces
and Applied Analysis 3 To prove our main results, for any h ∈ C J, E , we consider the Neumann boundary value problem NBVP of linear impulsive differential equation in E: −u′′ t Mu t h t , t ∈ J ′, −Δu′|t tk yk, k 1, 2, . . . , m, u′ 0 u′ 1 θ, 2.3 where M > 0, yk ∈ E, k 1, 2, . . . , m. Lemma 2.4. For any h ∈ C J, E , M > 0, and yk ∈ E, k 1, 2, . . . , m, the linear NBVP 2.3 has a unique soluti...
متن کاملON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *
The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.
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: Mediterranean Journal of Mathematics
سال: 2022
ISSN: ['1660-5454', '1660-5446']
DOI: https://doi.org/10.1007/s00009-021-01956-6