Infinitely many Solutions of Semi-Linear Elliptic Equation with a Logarithmic Nonlinear Term
2014 ◽
Vol 496-500
◽
pp. 2216-2219
Keyword(s):
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.
2014 ◽
Vol 526
◽
pp. 177-181
2011 ◽
Vol 09
(03)
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pp. 235-248
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1983 ◽
Vol 27
(1)
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pp. 1-30
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1953 ◽
Vol 39
(3)
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pp. 179-184
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Keyword(s):
1956 ◽
Vol 8
◽
pp. 203-219
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2012 ◽
Vol 55
(2)
◽
pp. 291-309
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2014 ◽
Vol 57
(3)
◽
pp. 779-809
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2014 ◽
Vol 33
(2)
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pp. 243-250
Keyword(s):
1999 ◽
Vol 24
(9-10)
◽
pp. 1731-1758
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Keyword(s):