Existence of positive solutions for a class of semipositone quasilinear problems through Orlicz-Sobolev space

Parametric and nonparametric A-Laplace problems: Existence of solutions and asymptotic analysis

“…For a N -function A : R → [0, +∞), we have the representation Of course, whenever ζ meets the above conditions, then A, given by (2), is a N-function. For our further use, we put ζ(ξ ) = a(ξ )ξ for all ξ ∈ [0, +∞) so that (2) reduces to…”

“…Also, the existence of multiple positive solutions for quasilinear elliptic problems with nonhomogeneous principal part a was established by Fukagai-Narukawa [8] in the Orlicz-Sobolev spaces. Very recently, Alves-De Holanda-Santos [2] proved the existence of positive weak solutions for a semipositone problem driven by a A-Laplace operator, with subcritical growth of the reaction. We recall that the Orlicz spaces are a genuine extension of L p spaces (1 p < +∞), whenever a N-function (that is, a convex, even function A : R → [0, +∞) satisfying A(t) = 0 if and only if t = 0, lim t→0 A(t) t…”

Existence of positive solutions for a parameter fractional $p$-Laplacian problem with semipositone nonlinearity

“…Indeed, they proved the existence of at least one positive solution if λ > 0 is sufficiently large. In [1], the authors proved the existence of positive solutions of a problem of semipositone type for the Φ-Laplacian through Orlicz-Sobolev spaces. Throughout this paper, C will denote positive constant, not the same at each occurrence.…”

Existence of positive solutions for a class of semipositone problems with Kirchhoff operator

“…A uniqueness result in exterior domains was proved in [14]. The version in Orlicz-Sobolev space was studied in [3]. Other interesting results can be seen in [1], [6], [9], [10], [11], [12], [17] and the references therein.…”