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In this paper, we consider the following class of the fractional p&q-Laplacian problem: (−Δ)psu+(−Δ)qsu+V(x)(|u|p−2u+|u|q−2u)+g(x)|u|r−2u=K(x)f(x,u)+h(u),x∈RN,V:RN→R+ is a potential function, and h:R→R is a perturbation term. We studied two cases: if f(x,u)… Click to show full abstract
In this paper, we consider the following class of the fractional p&q-Laplacian problem: (−Δ)psu+(−Δ)qsu+V(x)(|u|p−2u+|u|q−2u)+g(x)|u|r−2u=K(x)f(x,u)+h(u),x∈RN,V:RN→R+ is a potential function, and h:R→R is a perturbation term. We studied two cases: if f(x,u) is sublinear, by means of Clark’s theorem, which considers the symmetric condition about the functional, we get infinitely many solutions; if f(x,u) is superlinear, using the symmetric mountain-pass theorem, infinitely many solutions can be obtained.
Journal Title: Symmetry
Year Published: 2022
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