一类具变号权函数的椭圆型p-Laplace方程弱解的多重性
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摘要
考虑一类具变号权函数的椭圆型p-Laplace方程弱解的多重性,借助Nehari流形和对数型Sobolev不等式,证明了该问题至少存在两个非平凡弱解.
We considered the multiplicity of weak solutions for a class of p-Laplacian elliptic equations with sign-changing weight function.By means of Nehari's manifold and logarithmic Sobolev inequality,we proved that there were at least two nontrivial weak solutions to the problem.
We considered the multiplicity of weak solutions for a class of p-Laplacian elliptic equations with sign-changing weight function.By means of Nehari's manifold and logarithmic Sobolev inequality,we proved that there were at least two nontrivial weak solutions to the problem.
引文
[1]SQUASSINA M,SZULKIN A.Multiple Solutions to Logarithmic Schrodinger Equations with Periodic Potential[J].Calc Var Partial Differ Equ,2015,54(1):585-597.
[2]JI Chao,SZULKIN A.A Logarithmic Schrodinger Equation with Asymptotic Conditions on the Potential[J].J Math Anal Appl,2016,437(1):241-254.
[3]CHEN Hua,TIAN Shuying.Initial Boundary Value Problem for a Class of Semilinear Pseudo-parabolic Equations with Logarithmic Nonlinearity[J].J Differential Equations,2015,258(12):4424-4442.
[4]CHEN Hua,LUO Peng,LIU Gongwei.Global Solution and Blow-Up of a Semilinear Heat Equation with Logarithmic Nonlinearity[J].J Math Anal Appl,2015,422(1):84-98.
[5]JI Shanming,YIN Jingxue,CAO Yang.Instability of Positive Periodic Solutions for Semilinear Pseudo-parabolic Equations with Logarithmic Nonlinearity[J].J Differential Equations,2016,261(10):5446-5464.
[6]LE C N,LE X T.Global Solution and Blow-Up for a Class of p-Laplacian Evolution Equations with Logarithmic Nonlinearity[J].Acta Appl Math,2017,151(1):149-169.
[7]LE C N,LE X T.Global Solution and Blow-Up for a Class of Pseudo p-Laplacian Evolution Equations with Logarithmic Nonlinearity[J].Comput Math Appl,2017,73(9):2076-2091.
[8]TIAN Shuying.Multiple Solutions for the Semilinear Elliptic Equations with the Sign-Changing Logarithmic Nonlinearity[J].J Math Anal Appl,2017,454(2):816-828.
[9]BROWN K J,ZHANG Yanping.The Nehari Manifold for a Semilinear Elliptic Equation with a Sign-Changing Weight Function[J].J Differential Equations,2003,193(2):481-499.
[10]BROWN K J.The Nehari Mainfold for a Semilinear Elliptic Equation Involving a Sublinear Term[J].Calc Var Partial Differ Equ,2004,22(4):483-494.
[11]WU T F.Multiple Positive Solutions for a Class of Concave-Convex Elliptic Prbolems in Rn Involving Sign-Changing Weight[J].J Funct Anal,2010,258(1):99-131.
[12]DEL P M,DOLBEAULT J.Nonlinear Diffusions and Optimal Constants in Sobolev Type Inequalities:Asymptotic Behaviour of Equations Involving the p-Laplacian[J].C R Math Acad Sci Paris,2002,334(5):365-370.
[13]ZEIDLER E.Nonlinear Funtional Analysis and Its ApplicationsⅡ/B[M].New York:Springer-Verlag,1990.
[2]JI Chao,SZULKIN A.A Logarithmic Schrodinger Equation with Asymptotic Conditions on the Potential[J].J Math Anal Appl,2016,437(1):241-254.
[3]CHEN Hua,TIAN Shuying.Initial Boundary Value Problem for a Class of Semilinear Pseudo-parabolic Equations with Logarithmic Nonlinearity[J].J Differential Equations,2015,258(12):4424-4442.
[4]CHEN Hua,LUO Peng,LIU Gongwei.Global Solution and Blow-Up of a Semilinear Heat Equation with Logarithmic Nonlinearity[J].J Math Anal Appl,2015,422(1):84-98.
[5]JI Shanming,YIN Jingxue,CAO Yang.Instability of Positive Periodic Solutions for Semilinear Pseudo-parabolic Equations with Logarithmic Nonlinearity[J].J Differential Equations,2016,261(10):5446-5464.
[6]LE C N,LE X T.Global Solution and Blow-Up for a Class of p-Laplacian Evolution Equations with Logarithmic Nonlinearity[J].Acta Appl Math,2017,151(1):149-169.
[7]LE C N,LE X T.Global Solution and Blow-Up for a Class of Pseudo p-Laplacian Evolution Equations with Logarithmic Nonlinearity[J].Comput Math Appl,2017,73(9):2076-2091.
[8]TIAN Shuying.Multiple Solutions for the Semilinear Elliptic Equations with the Sign-Changing Logarithmic Nonlinearity[J].J Math Anal Appl,2017,454(2):816-828.
[9]BROWN K J,ZHANG Yanping.The Nehari Manifold for a Semilinear Elliptic Equation with a Sign-Changing Weight Function[J].J Differential Equations,2003,193(2):481-499.
[10]BROWN K J.The Nehari Mainfold for a Semilinear Elliptic Equation Involving a Sublinear Term[J].Calc Var Partial Differ Equ,2004,22(4):483-494.
[11]WU T F.Multiple Positive Solutions for a Class of Concave-Convex Elliptic Prbolems in Rn Involving Sign-Changing Weight[J].J Funct Anal,2010,258(1):99-131.
[12]DEL P M,DOLBEAULT J.Nonlinear Diffusions and Optimal Constants in Sobolev Type Inequalities:Asymptotic Behaviour of Equations Involving the p-Laplacian[J].C R Math Acad Sci Paris,2002,334(5):365-370.
[13]ZEIDLER E.Nonlinear Funtional Analysis and Its ApplicationsⅡ/B[M].New York:Springer-Verlag,1990.