In this paper, we
study the following Kirchhoff type equation with critical growth
where
stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si2.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=33fb950e2aefa5dbfdb99496994fc062" title="Click to view the MathML source">a>0,b≥0 and
stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si3.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=398727f33b6213eb3973e75ca1685996" title="Click to view the MathML source">Ω is a smooth bounded domain in
stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si4.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=ebd42ef49dd29d2195a05563abeb98a9" title="Click to view the MathML source">R3. When the real parameter
stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si5.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=cc0e9ea79a02c1bc6e6fa900b1777f5f" title="Click to view the MathML source">μ is larger than some positive con
stant, we inve
stigate the multiplicity of nontrivial solutions for the above problem with parameter
stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si6.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=f67cf5f117fda276f3542cb282631913" title="Click to view the MathML source">λ belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator
stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si7.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=338b67f8abe230159956e416aba2ebef" title="Click to view the MathML source">−△.