%0 Generic
%A  Wang Zhongxiang
%A  Jia Gao
%C Szeged
%D 2021
%F acta:75804
%K Kirchhoff-egyenlet, Differenciálegyenlet
%N 83
%T Existence and multiplicity of nontrivial solutions to the modified Kirchhoff equation without the growth and Ambrosetti-Rabinowitz conditions
%U http://acta.bibl.u-szeged.hu/75804/
%X The paper focuses on the modified Kirchhoff equation a + b Z RN |∇u| 2 dx� ∆u − u∆(u 2 ) + V(x)u = λ f(u), x ∈ R N, where a, b > 0, V(x) ∈ C(RN, R) and λ < 1 is a positive parameter. We just assume that the nonlinearity f(t) is continuous and superlinear in a neighborhood of t = 0 and at infinity. By applying the perturbation method and using the cutoff function, we get existence and multiplicity of nontrivial solutions to the revised equation. Then we use the Moser iteration to obtain existence and multiplicity of nontrivial solutions to the above original Kirchhoff equation. Moreover, the nonlinearity f(t) may be supercritical.
%Z Bibliogr.: p. 16-18. ; összefoglalás angol nyelven