An indefinite and critical concave—convex-type equation
2013 ◽
Vol 143
(1)
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pp. 169-184
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Keyword(s):
We analyse the multiplicity of non-negative solutions for the critical concave—convex-type equationwhere Ω is a bounded domain of ℝN, 1 < r < p and λ > 0, and μ is a real parameter. Combining minimization on the underlying Nehari manifold with energy estimates, we show that, under suitable conditions on a and b, three non-negative solutions may exist when λ is positive and sufficiently small and μ is in a right neighbourhood of μ1, the first weighted eigenvalue of the p-Laplacian. To the best of our knowledge, our multiplicity result is new, even in the semi-linear case p = 2.
2009 ◽
Vol 51
(3)
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pp. 513-524
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2020 ◽
Vol 150
(5)
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pp. 2682-2718
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2009 ◽
Vol 139
(1)
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pp. 183-192
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Keyword(s):
1999 ◽
Vol 129
(6)
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pp. 1157-1169
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2007 ◽
Vol 137
(2)
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pp. 333-347
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Keyword(s):
2014 ◽
Vol 91
(2)
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pp. 273-277
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1999 ◽
Vol 129
(1)
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pp. 153-163
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