Affiliation:
1. Xidian University
2. Northwest Normal University
Abstract
We prove existence of weak solutions of Neumann problem of nonhomogeneous elliptic system with asymmetric nonlinearities that may resonant at
−
∞
and superlinear at
+
∞
. The proof is based on Mawhin's coincidence theory and the product formula of Brouwer degree.
Reference16 articles.
1. R. A. Adams, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press, New York, 1975.
2. Nontrivial solutions for a Neumann problem with a nonlinear term asymptotically linear at −∞ and superlinear at +∞
3. Superlinear critical resonant problems with small forcing term
4. On a resonant and superlinear elliptic system
5. R. E. Gaines, J. L. Mawhin, Coincidence degree, and nonlinear differential equations, Lecture Notes in Mathematics, Vol. 568, Springer-Verlag, Berlin--New York, 1977.