Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces
نویسندگان
چکیده
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 solution u ∈ PC1 J, E ∩ C2 J ′, E given by u t ∫1 0 G t, s h s ds m ∑ k 1 G t, tk yk, 2.4
منابع مشابه
Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces
This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.
متن کاملMultiple positive solutions for second order impulsive boundary value problems in Banach spaces
By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.
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 کاملExistence and uniqueness of positive solutions for Neumann problems of second order impulsive differential equations
This work is concerned with the existence and uniqueness of positive solutions for Neumann boundary value problems of second order impulsive differential equations. The result is obtained by using a fixed point theorem of generalized concave operators. MSC: 34B18; 34B37
متن کاملExistence of positive solutions for a second-order p-Laplacian impulsive boundary value problem on time scales
In this paper, we investigate the existence of positive solutions for a second-order multipoint p-Laplacian impulsive boundary value problem on time scales. Using a new fixed point theorem in a cone, sufficient conditions for the existence of at least three positive solutions are established. An illustrative example is also presented.
متن کامل