English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We investigate the existence and multiplicity of weak solutions for anonlinear Kirchhoff type quasilinear elliptic system on the whole space$\mathbb{R}^N$. We assume that the nonlinear term satisfies the locallysuper-$(m_1,m_2)$ condition, that is,$\lim_{|(u,v)|\rightarrow+\infty}\frac{F(x,u,v)}{|u|^{m_1}+|v|^{m_2}}=+\infty\mbox{ for a.e. } x \in G$ where $G$ is a domain in $\mathbb{R}^N$, which isweaker than the well-known Ambrosseti-Rabinowitz condition and the naturallyglobal restriction,$\lim_{|(u,v)|\rightarrow+\infty}\frac{F(x,u,v)}{|u|^{m_1}+|v|^{m_2}}=+\infty\mbox{ for a.e. } x \in \mathbb{R}^N$. We obtain that system has at least oneweak solution by using the classical Mountain Pass Theorem. To a certainextent, our theorems extend the results of Tang-Lin-Yu [Journal of Dynamics andDifferential Equations, 2019, 31(1): 369-383]. Moreover, under the abovenaturally global restriction, we obtain that system has infinitely many weaksolutions of high energy by using the Symmetric Mountain Pass Theorem, which isdifferent from those results of Wang-Zhang-Fang [Journal of Nonlinear Sciencesand Applications, 2017, 10(7): 3792-3814] even if we consider the system on thebounded domain with Dirichlet boundary condition.

Existence and multiplicity of solutions for a class of Kirchhoff type  $(\Phi_1,\Phi_2)$-Laplacian system with locally super-linear condition in  $\mathbb{R}^N$