2019
DOI: 10.1016/j.jde.2019.04.039
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A sub-supersolution approach for some classes of nonlocal problems involving Orlicz spaces

Abstract: In the present paper we study the existence of solutions for some nonlocal problems involving Orlicz-Sobolev spaces. The approach is based on sub-supersolutions.

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Cited by 9 publications
(17 citation statements)
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“…For one thing, there are many ways to prove the sub-supersolution theorem. For example, Schaefer's fixed point theorem is used in [7,8,11,18,19], pseudomonotone operator theorem is used in [4,5,10], and the idea of monotone iteration is used in [20][21][22] to explore the sub-supersolution theorem of the equation. We must consider the applicability and feasibility of the above methods.…”
Section: Introductionmentioning
confidence: 99%
“…For one thing, there are many ways to prove the sub-supersolution theorem. For example, Schaefer's fixed point theorem is used in [7,8,11,18,19], pseudomonotone operator theorem is used in [4,5,10], and the idea of monotone iteration is used in [20][21][22] to explore the sub-supersolution theorem of the equation. We must consider the applicability and feasibility of the above methods.…”
Section: Introductionmentioning
confidence: 99%
“…This paper is concerned with the problem Here ρ ∈ C 1 : [0, +∞) → [0, +∞) and it satisfies (see [10]) (ρ 1 ) tρ(t) is differentiable for ∀t > 0, (ρ 2 ) lim t→0 + tρ(t) = 0, lim t→+∞ tρ(t) = +∞, and that there exist κ, s ∈ (1, N) such that (ρ 3 ) κ -1 ≤ (ρ(t)t) ρ(t) ≤ s -1, ∀t > 0. Note that (ρ 3 ) implies that (ρ 3 ) κ ≤ ρ(t)t 2 (t) ≤ s, ∀t > 0.…”
Section: Introductionmentioning
confidence: 99%
“…Problem (1.1) was proposed in [10] and generalizes some problems in [3,5,6,8,[17][18][19][20]. As the authors of [10] pointed out, there are some difficulties to study problem (1.1):…”
Section: Introductionmentioning
confidence: 99%
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