Logistic Type Equations on RN by a Squeezing Method Involving Boundary Blow‐Up Solutions

By Yihong Du, Li Ma. 2001

194 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9e584ff749574f9435011f2da851babd22553a30

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In Applied Mathematics

1. Mingxin Wang
2. L. D’Ambrosio
3. Rui Peng
4. Yihong Du
5. Zongming Guo
6. Junping Shi
7. Enzo Mitidieri
8. Zhigui Lin

In Mathematical Physics

1. Mingxin Wang
2. Yihong Du
3. Rui Peng
4. Junping Shi
5. L. D’Ambrosio
6. Zhigui Lin
7. Zongming Guo
8. Chengxia Lei

In Numerical Analysis

1. Zongming Guo
2. Rui Peng
3. Mingxin Wang
4. Zhigui Lin
5. Chengxia Lei
6. Qunying Zhang
7. Yihong Du
8. Junping Shi

Citations in the corpus

• Effect of a protection zone in the diffusive Leslie predator-prey model (2009, methodology): “1 of [16], it follows WR w̃n on BR(0).”
• On a Free Boundary Problem for a Two-Species Weak Competition System (2012, unknown): “2 of Du and Ma [14]), which implies that lim inft→+∞ u(x, t) ≥ 1 − k(1 + ε) uniformly in any compact subset of [0,∞).”
• The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor (2013, background): “can show v ≤ kv0k∞ +V(0), where V(x) is the unique boundary blow-up solution of −d2∆V = V(a2 −c2V) in B1(0), V = ∞ on ∂B1(0). (The existence and uniqueness of U and V is well known; see, for example, [6].)10 Y. DU AND Z.G. LIN In what follows, we discuss the comparison principle for (1.1). For a giv”
• Qualitative analysis of steady states to the Sel'kov model (2007, unknown): “We also like to mention that Du and Ma [4] established a similar result when the homogeneous Dirichlet boundary condition is concerned (see Lemma 2.2 there).”
• The spreading front of invasive species in favorable habitat or unfavorable habitat (2013, methodology): “1 in [12] that vR decreases to ũ as R approaches to ∞.”
• Liouville type results and eventual flatness of positive solutions for $p$-Laplacian equations (2002, background): “3) as λ → ∞ improve those obtained in [11] and [12].”
• Spreading–vanishing dichotomy in a diffusive logistic model with a free boundary, II☆ (2011, methodology): “1 of [12], we see that limt→+∞u(t, r) ≤ wRn(r) uniformly for r ∈ [0, Rn], which implies (by sending n →∞)”
• A priori estimates, positivity results, and nonexistence theorems for quasilinear degenerate elliptic inequalities (2010, background): “See for instance [33, 2,61] for applications to existence problems and [12,1,39,49,22,42,40] for related implications to geometrical and reaction diffusion problems.”
• A Free Boundary Problem for a Predator-prey Model with Double Free Boundaries (2013, unknown): “2 of [12], liml→∞wl(x) = β/θ uniformly in any compact subset of R.”
• A diffusive predator–prey model with a protection zone☆ (2006, background): “3); a more general version can be found in [23] (see Lemma 2.”
• Spreading-Vanishing Dichotomy in the Diffusive Logistic Model with a Free Boundary (2010, unknown): “1 of [9] to conclude that w ≥ Uk2 in [0,+∞), i.”