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34. Existence and multiplicity of solutions for a class of p-Kirchhoff-type equation RN

Author

Chen Lijuan, Xue Changfeng, and Wang Fangfang

Subjects
p-kirchhoff-type equation, (ps)c condition, symmetric mountain pass lemma, 35a15, Mathematics, QA1-939
Abstract

This article shows the existence and multiplicity of solutions for the following pp-Kirchhoff-type equation: a+b∫RN(∣∇u∣p+V(x)∣u∣p)dx(−△pu+V(x)∣u∣p−2u)=λg(x)∣u∣r−2u−h(x)∣u∣q−2u,inRN.\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{N}}\left({| \nabla u| }^{p}+V\left(x){| u| }^{p}){\rm{d}}x\right)\left(-{\bigtriangleup }_{p}u+V\left(x){| u| }^{p-2}u)=\lambda g\left(x){| u| }^{r-2}u-h\left(x){| u| }^{q-2}u,\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N}. where λ\lambda is a real parameter and 1

Published
2023
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