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

This paper proves the existence of nontrivial solution for two classes ofquasilinear systems of the type \begin{equation*} \left\{\; \begin{aligned}-\Delta_{\Phi_{1}} u&=F_u(x,u,v)+\lambda R_u(x,u,v)\;\text{ in } \Omega& \\-\Delta_{\Phi_{2}} v&=-F_v(x,u,v)-\lambda R_v(x,u,v)\;\text{ in } \Omega& \\u=v&=0\;\text{ on } \partial\Omega& \end{aligned} \right. \end{equation*} where$\lambda > 0$ is a parameter, $\Omega$ is a bounded domain in $\mathbb{R}^N$($N\geq 2$) with smooth boundary $\partial \Omega$. The first class we drop the$\Delta_2$-condition of the functions $\tilde{\Phi}_i$($i=1,2$) and assume that$F$ has a double criticality. For this class, we use a linking theorem withoutthe Palais-Smale condition for locally Lipschitz functionals combined with aconcentration-compactness lemma for nonreflexive Orlicz-Sobolev space. Thesecond class, we relax the $\Delta_2$-condition of the functions${\Phi}_i$($i=1,2$). For this class, we consider $F=0$ and $\lambda=1$ andobtain the proof based on a saddle-point theorem of Rabinowitz without thePalais-Smale condition for functionals Frechet differentiable combined withsome properties of the weak$^*$ topology.

Existence of solution for two classes of quasilinear systems defined on a non-reflexive Orlicz-Sobolev Spaces