caa a22 4500 606244581 CHVBK 20210128101331.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s12044-015-0250-7 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0250-7 Existence of positive weak solutions for ( p, q )-Laplacian nonlinear systems [Elektronische Daten] [SAMIRA ALA, G AFROUZI, A NIKNAM] We mainly consider the existence of a positive weak solution of the following system − Δ p u + u p − 2 u = λ g ( x ) a ( u ) + c ( x ) f ( v ) in Ω , − Δ q v + v q − 2 v = μ g ( x ) b ( v ) + c ( x ) h ( u ) in Ω , u = v = 0 on ∂ Ω , $$\left\{ \begin{array}[c]{cc}-{\Delta}_{p}u+\left\vert u\right\vert^{p-2}u=\lambda\left[ g(x)a(u)+c(x)f(v)\right] & ~\text{in}~{\Omega},\\-{\Delta}_{q}v+\left\vert v\right\vert^{q-2}v=\mu\left[ g(x)b(v)+c(x)h(u)\right] & ~\text{in}~ {\Omega},\\ u=v=0 & ~\text{on}~\partial{\Omega}, \end{array} \right. $$ where Δ p u= div(|∇u| p−2∇u),p,q >1 and λ,μ are positive parameters, and Ω⊂R N is a bounded domain with smooth boundary ∂Ω and g,c are nonnegative and continuous functions and f,h,a,b are C 1 nondecreasing functions satisfying a(0),b(0)≥0. We have proved the existence of a positive weak solution for λ, μ large when lim x → ∞ f M h x 1 q − 1 x p − 1 = 0 $$\lim\limits_{x\rightarrow\infty}\frac{f\left[ M\left( h\left( x\right) \right)^{\frac{1}{q-1}}\right]}{x^{p-1}}=0 $$ for every M > 0. Indian Academy of Sciences, 2015 p -Laplacian systems nationallicence sub-supersolution nationallicence positive weak solutions nationallicence ALA SAMIRA Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran aut AFROUZI G. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran aut NIKNAM A. Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran aut Proceedings - Mathematical Sciences Springer India 125/4(2015-11-01), 537-544 0253-4142 125:4<537 2015 125 12044 https://doi.org/10.1007/s12044-015-0250-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0250-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- ALA SAMIRA Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), Tehran, Iran aut NATIONALLICENCE 700 1- AFROUZI G. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran aut NATIONALLICENCE 700 1- NIKNAM A. Department of Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/4(2015-11-01), 537-544 0253-4142 125:4<537 2015 125 12044