Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47884220180701Solvability of Nonlinear Goursat Type Problem for Hyperbolic Equation with Integral Condition1982136516110.22034/kjm.2018.65161ENTaki EddineOussaeifDepartment of Mathematics and Informatics., The Larbi Ben M'hidi
University, Oum El Bouaghi, Algeria.AbdelfatahBouzianiDépartement de Mathématiques et Informatique, Université Larbi Ben M'hidi, Oum El Bouagui, B.P. 565, 04000, Algerie.Journal Article20180327This paper is concerned with the existence and uniqueness of a strong solution for linear problem by using a functional analysis method, which is based on an energy inequality and the density of the range of the operator generated by the problem. Applying an iterative process based on results obtained from the linear problem, we prove the existence and<br />uniqueness of the weak generalized solution of nonlinear hyperbolic Goursat problem with integral condition.http://www.kjm-math.org/article_65161_8fed2a0e71a8af7d76b734e82401f3b2.pdf