Blow-up solutions to the Monge–Ampère equation with a gradient term: sharp conditions for the existence and asymptotic estimates

Zhang, Xuemei; Feng, Meiqiang

doi:10.1007/s00526-022-02315-3

Cited by 11 publications

(2 citation statements)

References 44 publications

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“…Consequently, by using ( 21), (24) and Lemma 1, we conclude that A has at least one fixed point (x, y) ∈ P ∩ (Ω 2 \Ω 1 ) such that r 1 ≤ ∥(x, y)∥ ≤ r 2 .…”

Section: Resultsmentioning

confidence: 90%

“…In addition, some scholars have studied the existence of nontrivial radial convex solutions for a single Monge-Ampère equation or systems of such equations, utilizing the theory of topological degree, bifurcation techniques, the upper and lower solutions method, and so on. For further details, see [2][3][4][5][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Solvability Criterion for a System Arising from Monge–Ampère Equations with Two Parameters

Wang,

2024

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Monge–Ampère equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge–Ampère equations with two parameters is investigated based on the Guo–Krasnosel’skii fixed point theorem. In the end, two examples are given to illustrate our theoretical results.

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“…Consequently, by using ( 21), (24) and Lemma 1, we conclude that A has at least one fixed point (x, y) ∈ P ∩ (Ω 2 \Ω 1 ) such that r 1 ≤ ∥(x, y)∥ ≤ r 2 .…”

Section: Resultsmentioning

confidence: 90%