Second order three-point boundary value problems in abstract spaces

作者：Cichon Mieczyslaw^*; Salem Hussein A H

来源：Acta Mathematicae Applicatae Sinica-English Series, 2014, 30(4): 1131-1152.

DOI：10.1007/s10255-014-0429-1

• boundary value problem
• Pettis integral

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], eta and zeta are some positive constants. Denote by E a Banach space and assume, that u belongs to an Orlicz space i.e., u(center dot) a L (M) ([0, 1],a%26quot;e), where M is an N-function and c a E. %26lt;br%26gt;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.

• 出版日期2014-10