Kirchhoff型问题多个解的存在性及表示
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摘要
运用特殊函数法和相关的分析技巧,考虑了带线性项的Kirchhoff型问题,获得退化情形无穷多解的存在性及非退化情形多重解的存在性,并将解用固有函数表示出来.退化的Kirchhoff型问题无论是共振、近共振,还是非共振都存在无穷多解.
Kirchhoff-type problem with linear term were considered by using the methods of special function and analysis techniques.We obtain the existence of infinitely many solutions in degenerate case and multiple solutions in non-degenerate caseand all solutions are expressed on the basis of the eigenfunctions.There are infinitely many solutions in degenerate Kirchhoff-type problem whether it satisfies resonant,near resonance or non-resonant cases.
Kirchhoff-type problem with linear term were considered by using the methods of special function and analysis techniques.We obtain the existence of infinitely many solutions in degenerate case and multiple solutions in non-degenerate caseand all solutions are expressed on the basis of the eigenfunctions.There are infinitely many solutions in degenerate Kirchhoff-type problem whether it satisfies resonant,near resonance or non-resonant cases.
引文
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[5] 王跃,叶红艳,索洪敏.一类带Hardy-Sobolev临界指数的非局部问题正解的存在性[J].应用数学,2019,32(2):452-456.
[6] WANG Y,SUO H M,LEI C Y.Multiple positive solutions for a nonlocal problem involving critical exponent[J].Electronic Journal of Differential Equations,2017,275:1-11.
[7] LEI C Y,SUO H M,CHU C M.Three solutions of a Kirchhoff type problem involving critical growth and near resonance[J].Indian Journal of Pure & Applied Mathematics,2018,49(1):99-112.
[8] 丁凌,汪继秀,肖氏武.全空间上具有临界指数的Kirchhoff类方程无穷多个正解的存在性[J].南昌大学学报(理科版),2017,41(5):414-417.
[9] 容红,雷春雨,索洪敏.具有Hardy奇异项的近共振Kirchhoff方程正解的多重性[J].理论数学,2015(5):21-27.
[10] XIANG M Q,ZHANG B L,QIU H.Existence of solutions for a critical fractional Kirchhoff type problem in RN[J].Science China Mathematics,2017,60(9):1-14.
[11] 王跃.一类非局部问题解的存在性与多重性研究[D].贵阳:贵州民族大学,2018.
[12] 王跃,索洪敏,雷春雨.一类非局部问题正解的存在性和唯一性[J].应用泛函分析学报,2017,19(1):95-103.
[13] ZHANG J,ZHANG Z Y.Existence of nontrivial solution for a nonlocal problem with subcritical nonlinearity[J].Advances in Difference Equations,2018,359:1-8.
[2] KIRCHHOFF G R.Vorlesungen uber Matematische Physik:Mechanik[M].4th edn,Teubner,Leipzig,1897.
[3] 钟越,袁倩.一类非线性单边值问题解的存在及一致衰减性[J].西南民族大学学报(自然科学版),2018,44(6):632-639.
[4] 王跃,梁金平,索洪敏.一类非局部近共振问题多重解的存在性[J].西南大学学报(自然科学版),2018,40(4):53-58.
[5] 王跃,叶红艳,索洪敏.一类带Hardy-Sobolev临界指数的非局部问题正解的存在性[J].应用数学,2019,32(2):452-456.
[6] WANG Y,SUO H M,LEI C Y.Multiple positive solutions for a nonlocal problem involving critical exponent[J].Electronic Journal of Differential Equations,2017,275:1-11.
[7] LEI C Y,SUO H M,CHU C M.Three solutions of a Kirchhoff type problem involving critical growth and near resonance[J].Indian Journal of Pure & Applied Mathematics,2018,49(1):99-112.
[8] 丁凌,汪继秀,肖氏武.全空间上具有临界指数的Kirchhoff类方程无穷多个正解的存在性[J].南昌大学学报(理科版),2017,41(5):414-417.
[9] 容红,雷春雨,索洪敏.具有Hardy奇异项的近共振Kirchhoff方程正解的多重性[J].理论数学,2015(5):21-27.
[10] XIANG M Q,ZHANG B L,QIU H.Existence of solutions for a critical fractional Kirchhoff type problem in RN[J].Science China Mathematics,2017,60(9):1-14.
[11] 王跃.一类非局部问题解的存在性与多重性研究[D].贵阳:贵州民族大学,2018.
[12] 王跃,索洪敏,雷春雨.一类非局部问题正解的存在性和唯一性[J].应用泛函分析学报,2017,19(1):95-103.
[13] ZHANG J,ZHANG Z Y.Existence of nontrivial solution for a nonlocal problem with subcritical nonlinearity[J].Advances in Difference Equations,2018,359:1-8.