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《Journal of Sichuan Normal University(Natural Science)》 2009-06
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The Existence of Nontrivial Weak Solution of the Dirichlet Problem for Quasilinear Elliptic Equations

LIAO Wei1,2, PU Zhi-lin3(1. College of Mathematics and Information Science,Neijiang Normal College,Neijiang 641112,Sichuan; 2. Key Laboratory of Numerical Simulation of Sichuan Province,Neijiang Normal College,Neijiang 641112,Sichuan;3. College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066,Sichuan)  
In this paper the problem of asymptotically linearity for quasilinear elliptic equations corresponding to the nonsmooth functional is studied. By applying the critical point theory of the nonsmooth functional,truncation function method and the definition of weak solution,the existence of nontivial weak solution of the Dirichlet problem for the quasilinear elliptic equation is proved when the right hand member f(x,t) is asymptotically linear in t at infinity.
【Fund】: 四川省教育厅自然科学青年基金(07ZB110)资助项目
【CateGory Index】: O175.25
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