Electron. J. Differential Equations, Vol. 2022 (2022), No. 77, pp. 115.
Kirchhoff systems involving fractional
pLaplacian and singular nonlinearity
Mouna Kratou
Abstract:
In this work we consider the fractional Kirchhoff equations
with singular nonlinearity,
where Ω is a bounded domain in R^{N} with smooth boundary,
N> ps, s in (0,1), 0<α<1, 0< β< 1,
2αβ<p≤ pθ<q<p^{*}_{s},
p^{*}_{s}=2N/(N2s) is the fractional Sobolev exponent,
λ, μ are two parameters, a, b, c in C(overlineΩ)
are nonnegative weight functions,
M(t)=k+lt^{θ1} with k>0, l,θ≥1, and
(Δ)^{s}_{p} is the fractional plaplacian operator.
We prove the existence of multiple nonnegative solutions by
studying the nature of the Nehari manifold with respect to the parameters
λ and μ.
Submitted September 11, 2022. Published November 21, 2022.
Math Subject Classifications: 34B15, 37C25, 35R20.
Key Words: Kirchhofftype equations; fractional pLaplace operator;
Nehari manifold; singular elliptic system; multiple positive solutions,
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Mouna Kratou
College of sciences at Dammam
University of Imam Abdulrahman Bin Faisal
31441 Dammam, Saudi Arabia
email: mmkratou@iau.edu.sa

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