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In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a+b∫R3(−Δ)s2u2dx(−Δ)su+V(x)u=Q(x)f(u)+|u|2s∗−2u,x∈R3,where a,b>0 , (−Δ)s is the fractional Laplace operator with s∈(34,1) , V vanishes at infinity and… Click to show full abstract
In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a+b∫R3(−Δ)s2u2dx(−Δ)su+V(x)u=Q(x)f(u)+|u|2s∗−2u,x∈R3,where a,b>0 , (−Δ)s is the fractional Laplace operator with s∈(34,1) , V vanishes at infinity and 2s∗=63−2s . Under appropriate assumptions on f, we prove the existence of positive solution by using the variational method.
Keywords:
kirchhoff equation;
existence positive;
fractional kirchhoff;
infinity
Journal Title: Mathematische Nachrichten
Year Published: 2021
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Journal Title: Mathematische Nachrichten
Year Published: 2021
Link to full text (if available)
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recommendations!