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In this paper, we first study the fractional p‐Laplacian eigenvalue problem with indefinite weight (−Δp)su=λg(x)|u|p−2uinRN and prove that the problem exists a sequence of eigenvalues that converges to infinity and that the first eigenvalue is simple. Based on these results, we then consider the existence of infinitely many solutions for a class of indefinite weight problem with concave and convex nonlinearities.

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In this article, we devote to the finite dimensional reduction for the hyperviscous Navier-Stokes equation with L 2 force and prove the existence of an N-dimensional inertial manifold for this problem in T 3 .

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