带奇异项的次临界Schr?dinger方程的基态解
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摘要
主要研究一类带奇异项的次临界指标Schr?dinger方程■其中,N≥3,λ>0,0≤μ<2,40,方程都存在基态解.
In this paper,we study the following quasilinear Schr?dinger equation with the subcritical exponent and singular coefficient of the form:■where N≥3,λ>0,0≤μ<2,40 for the above equation.
In this paper,we study the following quasilinear Schr?dinger equation with the subcritical exponent and singular coefficient of the form:■where N≥3,λ>0,0≤μ<2,4
引文
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[5]RITCHIE B. Relativistic self-focusing and channel formation in laser-plasma interactions[J]. Phys Rev,1994,E50(2):687-689.
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[7]LAEDKE E,SPATSCHEK K,STENFLO L. Evolution theorem for a class of perturbed envelope soliton solutions[J]. J Math Phys,1983,24(2):2764-2769.
[8]POPPENBERG M,SCHMITT K,WANG Z. On the existence of soliton solutions to quasilinear Schr?dinger equations[J]. Calc Var Partial Differential Equations,2002,14(3):329-344.
[9]BEZERRA J,MIYAGAKI O,SOARES S. Soliton solutions for quasilinear Schr?dinger equations with critical growth[J]. J Diff Eqns,2010,248(4):722-744.
[10]COLIN M,JEANJEAN L. Solutions for a quasilinear Schr?dinger equation:a dual approach[J]. Nonlinear Anal:TMA,2004,56(2):213-226.
[11]LIU J,WANG Y,WANG Z. Soliton solutions for quasilinear Schr?dinger equations. II[J]. J Diff Eqns,2003,187(2):473-493.
[12]GHOUSSOUB N,YUAN C. Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents[J].Trans Am Math Soc,2000,352(12):5703-5743.
[13]FANG X,SZULKIN A. Multiple solutions for a quasilinear Schr?dinger equation[J]. J Diff Eqns,2013,254(4):2015-2032.
[14]FANG X. Positive solutions for quasilinear Schr?dinger equations in RN[J]. Commun Pure Appl Anal,2017,16(15):1603-1615.
[15] SILVA E,VIEIRA G. Quasilinear asymptotically periodic Schr?dinger equations with subcritical growth[J]. Nonlinear Anal:TMA,2010,72(6):2935-2949.
[16]BARTOLO P,BENCI V,FORTUNATO D. Abstract critical point theorems and applications to some nonlinear problems with“strong”resonance at infinity[J]. Nonlinear Anal:TMA,1983,7(9):981-1012.
[2]CHEN X L,SUDAN R N. Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma[J]. Phys Rev Lett,1993,70(70):2082-2085.
[3]KOSEVICH A M,IVANOV B A,KOVALEV A S. Magnetic solitons[J]. Phys Rep,1990,194(3):117-238.
[4]BRüLL L,LANGE H. Solitary waves for quasilinear Schr?dinger equations[J]. Exposition Math,1986,4(3):279-288.
[5]RITCHIE B. Relativistic self-focusing and channel formation in laser-plasma interactions[J]. Phys Rev,1994,E50(2):687-689.
[6]DE BOUARD A,HAYASHI N,SAUT J. Global existence of small solutions to a relativistic nonlinear Schr?dinger equation[J].Commun Math Phys,1997,189(1):73-105.
[7]LAEDKE E,SPATSCHEK K,STENFLO L. Evolution theorem for a class of perturbed envelope soliton solutions[J]. J Math Phys,1983,24(2):2764-2769.
[8]POPPENBERG M,SCHMITT K,WANG Z. On the existence of soliton solutions to quasilinear Schr?dinger equations[J]. Calc Var Partial Differential Equations,2002,14(3):329-344.
[9]BEZERRA J,MIYAGAKI O,SOARES S. Soliton solutions for quasilinear Schr?dinger equations with critical growth[J]. J Diff Eqns,2010,248(4):722-744.
[10]COLIN M,JEANJEAN L. Solutions for a quasilinear Schr?dinger equation:a dual approach[J]. Nonlinear Anal:TMA,2004,56(2):213-226.
[11]LIU J,WANG Y,WANG Z. Soliton solutions for quasilinear Schr?dinger equations. II[J]. J Diff Eqns,2003,187(2):473-493.
[12]GHOUSSOUB N,YUAN C. Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents[J].Trans Am Math Soc,2000,352(12):5703-5743.
[13]FANG X,SZULKIN A. Multiple solutions for a quasilinear Schr?dinger equation[J]. J Diff Eqns,2013,254(4):2015-2032.
[14]FANG X. Positive solutions for quasilinear Schr?dinger equations in RN[J]. Commun Pure Appl Anal,2017,16(15):1603-1615.
[15] SILVA E,VIEIRA G. Quasilinear asymptotically periodic Schr?dinger equations with subcritical growth[J]. Nonlinear Anal:TMA,2010,72(6):2935-2949.
[16]BARTOLO P,BENCI V,FORTUNATO D. Abstract critical point theorems and applications to some nonlinear problems with“strong”resonance at infinity[J]. Nonlinear Anal:TMA,1983,7(9):981-1012.