In the present paper, we study the following singular Kirchhoff problem [Formula presented], where Ω⊂RN is an open bounded domain, dimension N>2s with s∈(0,1), 2s ∗=2N∕(N−2s) is the fractional critical Sobolev exponent, parameter λ>0, exponent γ∈(0,1), M models a Kirchhoff coefficient, [Formula presented] is a positive weight, while g∈L∞(Ω) is a sign-changing function. Using the idea of Nehari manifold technique, we prove the existence of at least two positive solutions for a sufficiently small choice of λ. This approach allows us to avoid any restriction on the boundary of Ω.
Fiscella, A., Mishra, P. (2019). The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms. NONLINEAR ANALYSIS, 186, 6-32 [10.1016/j.na.2018.09.006].
The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms
Fiscella A
;
2019
Abstract
In the present paper, we study the following singular Kirchhoff problem [Formula presented], where Ω⊂RN is an open bounded domain, dimension N>2s with s∈(0,1), 2s ∗=2N∕(N−2s) is the fractional critical Sobolev exponent, parameter λ>0, exponent γ∈(0,1), M models a Kirchhoff coefficient, [Formula presented] is a positive weight, while g∈L∞(Ω) is a sign-changing function. Using the idea of Nehari manifold technique, we prove the existence of at least two positive solutions for a sufficiently small choice of λ. This approach allows us to avoid any restriction on the boundary of Ω.
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