The existence and non-existence of positive solutions to a singular quasilinear elliptic problem in

Sufficient conditions for the existence and asymptotic behaviour of solution to a quasi-linear elliptic problem

“…The above result has been generalized by Chai et al [2] and Qing and Yang [15] for more general class of functions. After these results, Goncalves and Silva [9] deal with more general conditions for the function g but in the case ⊂ R N they did not obtain the property (4) for the solution u.…”

“…D.-P. Covei A solution of the problem (1) will be a function u ∈ C 1 ( ) which satisfies |∇u| p−2 ∇u∇ϕ dx = λa(x)g(u)ϕ dx, ϕ ∈ C ∞ 0 ( ), (2) u(x) > 0, for all x ∈…”

“…Such problems have been extensively studied for both bounded or unbounded domains: Ye and Zhou [17], Goncalves and Santos [8], the author [3], Hai and Wang [11], Chai et al [2], Goncalves and Silva [9] and references therein. Our study is motivated by the recent works of [2,3,8,9], where the existence, non-existence and asymptotic behaviour of solutions for the problem (1) are solved in ⊆ R N .…”

“…Our study is motivated by the recent works of [2,3,8,9], where the existence, non-existence and asymptotic behaviour of solutions for the problem (1) are solved in ⊆ R N .…”

“…By construction of a suitable lower and upper solution, we intent, in this paper, to discover more ideas and techniques that in [2,3] in order to open the access for a more general class of function as in [9] in any situation ⊆ R N .…”