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 Imed Bachar Electronic Journal of Differential Equations , 2012, Abstract: We prove the existence of positive continuous solutions to the nonlinear fractional system $$displaylines{ (-Delta|_D) ^{alpha/2}u+lambda g(.,v) =0, cr (-Delta|_D) ^{alpha/2}v+mu f(.,u) =0, }$$ in a bounded $C^{1,1}$-domain $D$ in $mathbb{R}^n$ $(ngeq 3)$, subject to Dirichlet conditions, where $0  Mathematics , 2013, Abstract: Let$\Omega$be a smooth bounded domain in$\mathbb{R}^{N}$and let$m$be a possibly discontinuous and unbounded function that changes sign in$\Omega$. Let$f:\left[ 0,\infty\right) \rightarrow\left[ 0,\infty\right) $be a continuous function such that$k_{1}\xi^{p}\leq f\left(\xi\right) \leq k_{2}\xi^{p}$for all$\xi\geq0$and some$k_{1},k_{2}>0$and$p\in\left(0,1\right) $. We study existence and nonexistence of strictly positive solutions for nonlinear elliptic problems of the form$-\Delta u=m\left(x\right) f\left(u\right) $in$\Omega$,$u=0$on$\partial\Omega$.  Mathematics , 2004, DOI: 10.1016/j.anihpc.2004.09.001 Abstract: We study nonlinear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that the ergodic constant appears in the (possibly nonlinear) Neumann boundary conditions. We provide, for bounded domains, several results on the existence, uniqueness and properties of this ergodic constant.  Electronic Journal of Differential Equations , 2005, Abstract: Let$D$be an unbounded domain in$mathbb{R}^{n}$($ngeq 2$) with a nonempty compact boundary$partial D$. We consider the following nonlinear elliptic problem, in the sense of distributions, $$displaylines{ Delta u=f(.,u),quad u>0quad hbox{in }D,cr uig|_{partial D}=alpha varphi ,cr lim_{|x|o +infty }frac{u(x)}{h(x)}=eta lambda , }$$ where$alpha ,eta,lambda $are nonnegative constants with$alpha +eta >0$and$varphi $is a nontrivial nonnegative continuous function on$partial D$. The function$f$is nonnegative and satisfies some appropriate conditions related to a Kato class of functions, and$h$is a fixed harmonic function in$D$, continuous on$overline{D}\$. Our aim is to prove the existence of positive continuous solutions bounded below by a harmonic function. For this aim we use the Schauder fixed-point argument and a potential theory approach.