Khalil, JiyidAlkharraz, Modhi Yousef20217099https://hdl.handle.net/20.500.14154/27112في هذه الرسالة نقوم بدراسة مسألة اهليجيه شبه حرجة وحرجة لنيومان منبثقة من نظام Segel-Keller الناشئ عند الانجذاب الكيميائي ونظهر ان هنالك دائما حلا غير بديهي مركزا عند نقطة حدودية وذلك إذا كنا قريبين من الأس الحرج للمسألةThis thesis is devoted to study an elliptic Neumann problem with critical nonlinearity. −∆u + µu = u N+2 N−2 +ε , u > 0 in Ω; ∂u ∂n = 0 on ∂Ω, where Ω is a smooth bounded domain in R N , N ⩾ 4, ε is small real number and µ is a constant positive function. We prove that for ε positive small, there exists a nontrivial solution which blows up to a point a ∈ ∂Ω which achieves the upper bounded of the boundary mean curvature. We also prove that when ε is negative small and Ω is not convex, there exists a nontrivial solution which blows up to a point a ∈ ∂Ω which achieves the lower bound of the boundary mean curvature. Lastly, we consider the critical case, i.e ε = 0, and µ is a small positive constant and we investigate numerical positive radial solutions on the ball.97enThesis