| 杨洁勤,陈会文,刘冬元,肖可.一类带渐近位势半线性椭圆方程解的多重性研究[J].南华大学学报(自然科学版),2019,33(6):41~45.[YANG Jieqin,CHEN Huiwen,LIU Dongyuan,XIAO Ke.Multiple Solutions for a Class of Semilinear Elliptic Equations with Asymptotical Potentials[J].Journal of University of South China(Science and Technology),2019,33(6):41~45.] |
| 一类带渐近位势半线性椭圆方程解的多重性研究 |
| Multiple Solutions for a Class of Semilinear Elliptic Equations with Asymptotical Potentials |
| 投稿时间：2019-07-27 |
| DOI： |
| 中文关键词: 半线性椭圆方程 渐近线性 临界点理论 |
| 英文关键词:semilinear elliptic equations asymptotically linear critical point theory |
| 基金项目:湖南省教育厅基金资助项目(15C1171) |
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| 摘要点击次数: 332 |
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| 中文摘要: |
| 讨论了半线性椭圆方程-Δu+a(x)u=g(x,u)解的多重性。其中非线性项g的原函数是渐近二次增长的,a可以符号变换。通过使用临界点定理,选取了一些新的条件来保证上述问题解的存在多重性,改善了以前的研究结果。 |
| 英文摘要: |
| The multiplicity solutions for the semilinear elliptic equations -Δu+a(x)u=g(x,u) were discussed.The primitive of the nonlinearity g is of asymptotically quadratic growth and the potential a is allowed to be sign-changing.Some new conditions are established by using critical point theory to guarantee multiple solutions of the above problem,which improve research results at present. |
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