A study of nonlinear elliptic equations with variational methods

Research Project

Project/Area Number	23740130
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Multi-year Fund
Research Field	Global analysis
Research Institution	Waseda University
Principal Investigator	HIRATA Jun 早稲田大学, 理工学術院, その他 (10580483)
Project Period (FY)	2011-04-28 – 2016-03-31
Project Status	Completed (Fiscal Year 2015)
Budget Amount *help	¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000) Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords	変分法 / 非線型楕円型方程式 / 楕円型方程式 / 微分方程式
Outline of Final Research Achievements	We study nonlinear elliptic equations and in paticular the existence of non-trivial solutions. We succeed to show the existece of positive solutions in the situation where the corresponding functional does not satisfy the Palais-Smale condition. We give a new estimate for functionals which enable us to show the existece of critical points. As its application, we also study singular perturbation problems.

Report

(6 results)