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On Kirchhoff type problems involving critical and singular nonlinearities

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Lei C.-Y., Chu C.-M., Suo H.-M., Tang C.-L.

Annales Polonici Mathematici

2015

tom 114

nr 3

269-291

In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧$-(a + b∫_{Ω} |∇u|²dx)Δu = u⁵ + λ u^{q-1}/|x|^{β}$ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Chu C.-M.

1 Lei C.-Y.

1 Suo H.-M.

1 Tang C.-L.

1 2015

Wyniki wyszukiwania

On Kirchhoff type problems involving critical and singular nonlinearities