Infinitely many Solutions of Semi-Linear Elliptic Equation with a Logarithmic Nonlinear Term

Yuan Li; Jiang Qin

doi:10.4028/www.scientific.net/AMM.496-500.2216

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 496-500Infinitely many Solutions of Semi-Linear Elliptic...

Infinitely many Solutions of Semi-Linear Elliptic Equation with a Logarithmic Nonlinear Term

Abstract:

The semi-linear elliptic equation is an important model in Mathematic, Physics. In this paper, we study the Dirichlet problem of semi-linear elliptic equation with a logarithmic nonlinear term. By using the logarithmic Sobolev inequality, mountain pass theorem and perturbation theorem, we obtain infinitely many nontrivial weak solutions, and also the energy of the solution is positive.

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Periodical:

Applied Mechanics and Materials (Volumes 496-500)

Pages:

2216-2219

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.496-500.2216

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Online since:

January 2014

Authors:

Yuan Li, Jiang Qin

Keywords:

Logarithmic Sobolev Inequality, Mountain Pass Theorem, Perturbation

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References

[1] A. Ambrosetti, P.H. Rabinowitz, Dual variational methodsin critical point theory and applications, J. Funct. Anal. 14(1973), pp.349-381.

DOI: 10.1016/0022-1236(73)90051-7

Google Scholar

[2] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponent, Comm. Pure Appl. Math. 36, (1983), pp.437-477.

DOI: 10.1002/cpa.3160360405

Google Scholar

[3] M. Struwe: Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamitonian Systems. Second ed. Springer-Verlag, (2009).

Google Scholar

[4] L. Gross: Logarithmic Sobolev inequalities, Amer. J. Math. 97(1976), pp.1061-1083.

Google Scholar

[5] E.A. Carlen: Superadditivity of Fisher's information and logarithmic Sobolev inequalities, J. Funct. Anal. 101(1991), pp.194-211.

DOI: 10.1016/0022-1236(91)90155-x

Google Scholar

[6] L.C. Evans: Partial differential equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society (1998), pp.326-337.

Google Scholar

[7] Wen-Ming, Zou: On finding sign-changing solutions, J. Funct . Anal. 234(2006), pp.364-419.

Google Scholar