一类分数阶基尔霍夫方程的无穷多解
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摘要
研究带有分数阶p(x)-拉普拉斯算子的基尔霍夫方程Dirichlet边值问题。当非线性项超线性增长时,利用临界点理论中的喷泉定理,得到了无穷多高能量解存在的充分条件。
Dirichlet boundary value problem for Kirchhoff equation with fractional p(x)-Laplacian operator is studied. When the nonlinear term is growing superlinearly, some sufficient conditions for the existence of infinitely many high energy solutions are obtained by using the fountain theorem in critical point theory.
Dirichlet boundary value problem for Kirchhoff equation with fractional p(x)-Laplacian operator is studied. When the nonlinear term is growing superlinearly, some sufficient conditions for the existence of infinitely many high energy solutions are obtained by using the fountain theorem in critical point theory.
引文
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[13] BISCI G,SERVADEL R.A bifurcation result for non-local fractional equations[J].Analysis Applications,2015,13(4):371-394.
[14] XIANG M ,ZHANG B L,GUO X Y.Infinitely many solutions for a fractional Kirchhoff type problem via fountain theorem [J].Nonlinear Analysis:Theory Methods Applications,2015,120(3):299-313.
[15] 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.
[16] FISCELLA A,PINAMONTI A,VECCHI E.Multiplicity results for magnetic fractional problems [J].Journal of Differential Equations,2017,15(8):4617-4633.
[17] AMBROSIO V,BISCI G.Periodic solutions for nonlocal fractional equations [J].Communications on Pure & Applied Analysis,2017,16(1):331-344.
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[21] KAUFMANN U,ROSSI J,VIDAL R.Fractional Sobolev spaces with variable exponents and fractional p(x)- Laplacians [J].Electronic Journal of Qualitative Theory of Differential Equations,2017,76(1):1-10.
[2] PERERA K,ZHANG Z T.Nontrivial solutions of Kirchhoff-type problems via the Yang index [J].Journal of Differential Equations,2006,221(1):246-255.
[3] ZHANG Z T,PERERA K.Sign changing solutions of Kirchoff type problems via invariant sets of descent flow [J].Journal of Mathematical Analysis and Applications,2006,317(2):456-463.
[4] MAO A M,ZHANG Z T.Sign changing and multiple solutions of Kirchhoff type problems without the P.S.condition [J].Nonlinear Analysis:Theory Methods Applications,2009,70(3):1275-1287.
[5] WU X.Existence of nontrivial solutions and high energy solutions for Schrodinger Kirchhoff-type equations in RN [J].Nonlinear Analysis:Real World Applications,2011,12(2):1278-1287.
[6] JIN J,WU X.Infinitely many radial solutions for Kirchhoff-type problems in RN [J].Journal of Mathematical Analysis and Applications,2010,369(2):564-574.
[7] LIU J,LIAO J F,TANG C L.Positive solutions for Kirchhoff-type equations with critical exponent in RN [J].Journal of Mathematical Analysis and Applications,2015,429(1):1153-1172.
[8] LIU J,LIAO J F,TANG C L.The existence of a ground-state solution for a class of Kirchhoff-type equations in RN [J].Proc Roy Soc Edinburgh Sect A,2016,146(2):371-391.
[9] FISCELLA A,VALDINOCI E.A critical Kirchhoff type problem involving a nonlocal operator [J].Nonlinear Analysis:Theory Methods Applications,2014,94(1):156-170.
[10] RUZICKA M.Electrorheologial fluids:modeling and mathematial theory [M].Berlin:Springer-Verlag,2000.
[11] 程伟,柏仕坤,徐家发.RN上的分数p-Laplacian方程弱解的存在性[J].中山大学学报(自然科学版),2018,57(1):49-54.CHENG W,BAI S K,XU J F.Existence of weak solutions for a fractional p-Laplacian in RN [J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2018,57(1):49-54.
[12] 程伟,徐家发.一类分数阶哈密顿系统非平凡解的存在性[J].中山大学学报(自然科学版),2016,55(5):21-26.CHENG W,XU J F.Existence of nontrivial solutions for a class of fractional Hamiltonian systems[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2016,55(5):21-26.
[13] BISCI G,SERVADEL R.A bifurcation result for non-local fractional equations[J].Analysis Applications,2015,13(4):371-394.
[14] XIANG M ,ZHANG B L,GUO X Y.Infinitely many solutions for a fractional Kirchhoff type problem via fountain theorem [J].Nonlinear Analysis:Theory Methods Applications,2015,120(3):299-313.
[15] 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.
[16] FISCELLA A,PINAMONTI A,VECCHI E.Multiplicity results for magnetic fractional problems [J].Journal of Differential Equations,2017,15(8):4617-4633.
[17] AMBROSIO V,BISCI G.Periodic solutions for nonlocal fractional equations [J].Communications on Pure & Applied Analysis,2017,16(1):331-344.
[18] IANNIZZOTTO A,PAPAGEORGIOU N.Existence and multiplicity results for resonant fractional boundary value problems [J].Discrete and Continuous Dynamical Systems(Series S),2017,11(3):1-19.
[19] BARTSCH T.Infinitely many solutions of a symmetric Dirichlet problem [J].Nonlinear Analysis:Theory Methods Applications,1993,20(20):1205-1216.
[20] BAHROUNI A,RADULESCU D.On a new fractional Sobolev space and spplications to nonlocal variational problems with variable exponent [J].Discrete and Continuous Dynamical Systems(Series S),2018,11(3):1-17.
[21] KAUFMANN U,ROSSI J,VIDAL R.Fractional Sobolev spaces with variable exponents and fractional p(x)- Laplacians [J].Electronic Journal of Qualitative Theory of Differential Equations,2017,76(1):1-10.