Consider the following fractional Kirchhoff equations involving critical exponent: 1+λ1∫RN(|(−Δ)α2u|2+V(x)u2)dx[(−Δ)αu+V(x)u]=k(x)f(u)+λ2|u|2α∗−2uinRN, where (−Δ)α is the fractional Laplacian operator with α∈(0,1), N≥2, λ1≥0, λ2>0 and 2α∗=2N/(N−2α) is the critical Sobolev exponent, V(x) and k(x) are functions satisfying some extra hypotheses. Based on the principle of concentration compactness in the fractional Sobolev space, the minimax arguments, Pohozaev identity, and suitable truncation techniques, we obtain the existence of a nontrivial weak solution for the previously mentioned equations without assuming the Ambrosetti–Rabinowitz condition on the subcritical nonlinearity f. Copyright © 2016 John Wiley & Sons, Ltd.

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fractional laplacian operator truncation concentration compactness 01 n2 10 ambrosettirabinowitz condition critical exponent 11rn2u2vxu2dxuvxukxfu2u22uinrn the subcritical nonlinearity fractional kirchhoff equations minimax arguments pohozaev identity weak

Xia Zhang, Chao Zhang,.Existence of solutions for critical fractional Kirchhoff problems. 39 (15),.

Xia Zhang, Chao Zhang,"Existence of solutions for critical fractional Kirchhoff problems" 39

Xia Zhang, Chao Zhang,"Existence of solutions for critical fractional Kirchhoff problems"