Multiple solutions results for two-point boundary value problem with resonance
Wenming Zou
In this paper we prove the existence of multiple solutions for two-point boundary value problem, which is resonant type both at origin and at infinity, and with higher eigenvalue and unbounded nonlinear terms. Our main ingredients are Morse theory and the computations of critical groups.
keywords: Morse index critical groups resonance Two-point boundary value problem Betti number.
The Nehari manifold for fractional systems involving critical nonlinearities
Xiaoming He Marco Squassina Wenming Zou
We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of the Nehari manifold, we prove that the system admits at least two positive solutions when the pair of parameters $(\lambda,\mu)$ belongs to a suitable subset of $R^2$.
keywords: Nehari manifold. concave-convex nonlinearities Fractional systems

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