Existence and Multiplicity of Solutions for the Semi-Linear Dirichlet Problem with a Logarithmic Nonlinear Term

Yuan Li; Ai Hui Sheng

doi:10.4028/www.scientific.net/AMM.526.177

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 526Existence and Multiplicity of Solutions for the...

Existence and Multiplicity of Solutions for the Semi-Linear Dirichlet Problem with a Logarithmic Nonlinear Term

Abstract:

The Dirichlet problem with logarithmic nonlinear term doesn't satisfy (A.R) condition. By using the variant mountain pass theorem and perturbation theorem of variational methods, the existence of nontrivial solutions are established for . We also introduce some deformation of equation with a logarithmic nonlinear term, the sign-changing solution, the Nehari manifold theory, bifurcation theory, improve the theory of variational methods.

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Periodical:

Applied Mechanics and Materials (Volume 526)

Pages:

177-181

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.526.177

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Online since:

February 2014

Authors:

Yuan Li*, Ai Hui Sheng

Keywords:

Multiplicity of Solutions, Semi-Linear Dirichlet Problem, Variant Mountain Pass Theorem

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