Jiaquan Liu

On the system of p-Laplacian equations with critical growth

In this paper, we consider the system of p-Laplacian equations with critical growth − Δpuj = μj|uj|p−2u j +∑i=1kβ ij|ui|p∗ 2|uj|p∗ 2 −2uj,inxa0Ω,uj = 0, onxa0∂Ω,j = 1,…,k, where Ω is a bounded smooth domain in ℝN, 1 2, 0 0,βij = βji ≤ 0, for i≠j. The existence of infinitely many sign-changing solutions is proved by the truncation method and by the concentration analysis on the approximating solutions, provided N > p + p2.

Relationship of the morse index and the

We consider the second order strongly indefinite differential nsystem with superlinearities. By using the approximation method of nfinite element, we show that bounds on solutions of the nrestriction functional onto finite dimensional subspace are nequivalent to bounds on their relative Morse indices. The obtained nresults can be used to establish a Morse theory for strongly nindefinite functionals with superlinearities.