TY  - GEN
TI  - Existence and multiplicity of nontrivial solutions to the modified Kirchhoff equation without the growth and Ambrosetti-Rabinowitz conditions
SN  - 1417-3875
ID  - acta75804
N1  - Bibliogr.: p. 16-18. ; összefoglalás angol nyelven
N2  - The paper focuses on the modified Kirchhoff equation a + b Z RN |?u| 2 dx? ?u ? u?(u 2 ) + V(x)u = ? f(u), x ? R N, where a, b > 0, V(x) ? C(RN, R) and ? < 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.
UR  - http://acta.bibl.u-szeged.hu/75804/
AV  - public
Y1  - 2021///
CY  - Szeged
A1  -  Wang Zhongxiang
A1  -  Jia Gao
KW  - Kirchhoff-egyenlet
KW  -  Differenciálegyenlet
EP  - 18
ER  -