Fractional Kirchhoff problem with critical indefinite nonlinearity

We study the existence and multiplicity of positive solutions for a family of fractional Kirchhoff equations with critical nonlinearity of the form where is a smooth bounded domain, and . Here M is the Kirchhoff coefficient and is the fractional critical Sobolev exponent. The parameter λ is positive and the is a real valued continuous function which is allowed to change sign. By using a variational approach based on the idea of Nehari manifold technique, we combine effects of a sublinear and a superlinear term to prove our main results.