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Nonnegative solutions for a class of semipositone nonlinear elliptic equations in bounded domains of Rn

Bachar Imed, Mâagli Habib, Eltayeb Hassan

Opuscula Mathematica

2022

Vol. 42, no. 6

793--803

In this paper, we obtain sufficient conditions for the existence of a unique nonnegative continuous solution of semipositone semilinear elliptic problem in bounded domains of Rn (n ≥ 2). The global behavior of this solution is also given.

Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions

Hai D. D., Wang X.

Opuscula Mathematica

2019

Vol. 39, no. 5

675--689

We prove the existence of positive solutions for the p-Laplacian problem [formula] where [formula] can be nonlinear, i=1,2 , f:(0,∞)→R is p-superlinear or p-sublinear at ∞ and is allowed be singular (±∞) at 0, and λ is a positive parameter.