Existence results for a problems involving Hardy Potentials

الموضوعات

علوم بحتة وطبيعية

الملخص

The objective of our work is to study the Hardy inequality, Then we try to apply it to the following elliptic linear problem −∆u = γux2 + f(x) in Ωu = 0 on ∂Ωwhere f ∈ L2(Ω), 0 ∈ Ω, γ is a real parameter.To prove that it admits a unique weak solution by using Lax Milligram theorem.Then we have the following some elliptic problems involving Hardy potential −∆u = γu|x|2 + f(x,u) in Ωu = 0 on ∂Ωwhere Ω ⊂ RN (N > 2) be open and bounded, 0 ∈ Ω,γ is a real parameter.Where we study the existence at least non-trivial weak solution using Mountain-Passtheorem, that is the associated functional Jγ admits at least a non trivial critical point.We present the following a class of Kirchhoff type problem involving Hardy type potentials −M(RΩ |∇u|2dx)∆u =µx2 a(x)u + λf(x,u) in Ωu = 0 on ∂Ωwhere Ω ⊂ RN (N ≥ 3) is bounded domain with smooth boundary ∂Ω, 0 ∈ Ω,M : R+0 → R is continuous and increasing function with R+0:= [0,+∞), the functiona : Ω → R may change sign, λ is positive parameter,0 ≤ µ < 1CN,2, where CN,2 =2N−2 2is optimal constant in the Hardy Inequality.

روابط وملفات

التعريف والنوع

رقم الوثيقة

eec44d54-06af-4f8b-ad72-2dbb2916391d

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

ماستر (LMD)

نوع الملف

pdf text

أسماء الملفات

2372636_1.pdf

بيانات النشر

ألقاب المؤلفين

[{"name_ar":" Achouak Bouchellig","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"Abdelhak Mokhtari ","title_ar":"اشراف","title_en":"Supervision"}]

اللغة

English

المصدر والدورية

اسم المصدر

Existence results for a problems involving Hardy Potentials

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Hardy potentialsVariational methodsCritical pointWeak solutionmountain pass theorem.Kirchhoff type problemHardy type potentialSub-linear non-linearityMultiple solutionsThree critical points theorem

إشراف وإعداد

الإشراف

Abdelhak Mokhtari

الإعداد

Achouak Bouchellig

الاقتباسات الببليوغرافية