Journal
ADVANCES IN NONLINEAR ANALYSIS
Volume 8, Issue 1, Pages 267-277Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/anona-2016-0240
Keywords
Kirchhoff type equations; asymptotically linear; ground state solution; variational methods
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Funding
- NSFC [11301181]
- China Postdoctoral Science Foundation
- Young Teachers Foundation of BTBU [QNJJ2016-15]
- Natural Science Foundation of Heilongjiang Province of China [A201306]
- Research Foundation of Heilongjiang Educational Committee [12541667]
- Doctoral Research Foundation of Heilongjiang Institute of Technology [2013BJ15]
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In this paper, we study the following Kirchhoff type equation: -(1 + b integral(RN) vertical bar del u vertical bar(2) dx)Delta u + u = a(x)f(u) in R-N, u is an element of H-1(R-N), where N >= 3, b > 0 and f(s) is asymptotically linear at infinity, that is, f(s) similar to O(s) as s -> +infinity. By using variational methods, we obtain the existence of a mountain pass type solution and a ground state solution under appropriate assumptions on a(x).
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