Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity
Keyword(s):
Abstract We are concerned with the following quasilinear elliptic equation $$\begin{array}{} \displaystyle -{\it\Delta} u-{\it\Delta}(u^{2})u=\mu |u|^{q-2}u+|u|^{2\cdot 2^*-2}u, u\in H_0^1({\it\Omega}), \end{array}$$(QSE) where Ω ⊂ ℝN is a bounded domain, N ≥ 3, qN < q < 2 ⋅ 2∗, 2∗ = 2N/(N – 2), qN = 4 for N ≥ 6 and qN = $\begin{array}{} \frac{2(N+2)}{N-2} \end{array}$ for N = 3, 4, 5, and μ is a positive constant. By employing the Nehari manifold and the Lusternik-Schnirelman category theory, we prove that there exists μ* > 0 such that (QSE) admits at least catΩ(Ω) positive solutions when μ ∈ (0, μ*).
2005 ◽
Vol 71
(3)
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pp. 377-386
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EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO CERTAIN QUASILINEAR ELLIPTIC EQUATIONS IN A BALL
2006 ◽
Vol 26
(1)
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pp. 125-133
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2001 ◽
Vol 64
(1)
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pp. 149-156
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2006 ◽
Vol 136
(6)
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pp. 1131-1155
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