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Acta Mathematicae Applicatae Sinica, English Series 2014, Vol. 30 Issue (4) :1131-1152    DOI: 10.1007/s10255-014-0429-1
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Second Order Three-point Boundary Value Problems in Abstract Spaces
Mieczys?aw Cichoń1, Hussein A.H. Salem2
1 Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań, Poland;
2 Department of Mathematics, Faculty of Sciences, Alexandria University, Egypt
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Abstract In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundary value problem

The coefficient functions a and b are continuous real-valued functions on [0, 1], η and ζ are some positive constants. Denote by E a Banach space and assume, that u belongs to an Orlicz space i.e., u(·)∈LM([0, 1],R), where M is an N-function and cE.
We search for solutions of the above problem in the Banach space of continuous functions C([0, 1],E) with the Pettis integrability assumptions imposed on f. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.
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Keywordsboundary value problem   Pettis integral     
Abstract: In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundary value problem

The coefficient functions a and b are continuous real-valued functions on [0, 1], η and ζ are some positive constants. Denote by E a Banach space and assume, that u belongs to an Orlicz space i.e., u(·)∈LM([0, 1],R), where M is an N-function and cE.
We search for solutions of the above problem in the Banach space of continuous functions C([0, 1],E) with the Pettis integrability assumptions imposed on f. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.
Keywordsboundary value problem,   Pettis integral     
Received: 2012-02-07;
Cite this article:   
.Second Order Three-point Boundary Value Problems in Abstract Spaces[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2014,V30(4): 1131-1152
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-014-0429-1      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2014/V30/I4/1131
 
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