On global bifurcation for quasilinear elliptic systems on bounded domains

By Junping Shi, Xuefeng Wang. 2009

354 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/5d635c9c58ccd1ea6e8e750acb27ac108297efda

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Junjie Wei
2. Jinfeng Wang
3. Junping Shi
4. Alina Chertock
5. Yongli Song
6. Xiaosong Tang
7. Xingfu Zou
8. Wendi Wang

In Modeling and Simulation

1. Junjie Wei
2. Xingfu Zou
3. Yongli Song
4. Xiaosong Tang
5. Jinfeng Wang
6. Junping Shi
7. Feng-Bin Wang
8. Wendi Wang

In Public Health, Environmental and Occupational Health

1. Junping Shi
2. Junjie Wei
3. Jinfeng Wang
4. Yongli Song
5. Xingfu Zou
6. Xiaosong Tang
7. Ping Liu
8. Yuwen Wang

Citations in the corpus

• Non-existence of non-constant positive steady states of two Holling type-II predator–prey systems: Strong interaction case (2009, neutral): “The global properties of the bifurcating branches have also been considered (see [1,4,6,38]), following the celebrated global bifurcation theorem of Rabinowitz [34].”
• Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey (2011, positive): “Instead we use global bifurcation theory developed in [41,48] to obtain the existence of nonconstant steady state solutions with certain eigen-modes.”
• Steady states and dynamics of an autocatalytic chemical reaction model with decay (2012, background): “Compared with the unilateral global bifurcation theorems in [18,33], the result here excludes the possibility of Σ+ meeting Σ− as this case is included in the second alternatives in Theorem 4.”
• ON A CHEMOTAXIS MODEL WITH SATURATED CHEMOTACTIC FLUX (2012, methodology): “In §5, we study one-dimensional (1-D) steady-state solutions and use both the local [11] and global [30, 34] bifurcation theories to investigate existence of nontrivial steady states.”
• Qualitative analysis of a Lotka-Volterra competition system with advection (2014, background): “Denoting u = (u, v)T, we can write (3.8) as D(u,v)F(u0, v0, χ)(u, v) = A0(u)u′′ + F0(x,u,u′), where A0(u) = ( D1 u0φ(v0) 0 D2 ) and F0 = ( (a1 − 2b1u0 − c1v0)u− c1u0v (a2 − b2u0 − 2c2v0)v − b2uv0 ) , then we see that operator (3.8) is elliptic; moreover it is strongly elliptic and satisfies the Agmo”
• Global bifurcation of solutions for a predator–prey model with prey‐taxis (2015, methodology): “To this end, we will first state the following result of Shi and Wang [11], which is another version of the well-known Crandall–Rabinowitz’s bifurcation theorem [12].”
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system ✩ (2009, background): “The theory in [44] also holds for higher-dimensional domain Ω and X = W 2,p(Ω) where p > 2.”
• Bifurcation analysis of reaction–diffusion Schnakenberg model (2013, background): “From the global bifurcation theorem in Shi and Wang [14], n is contained in a global branch Cn of solutions.”
• Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of Cima chemical reactions (2013, background): “2 in Appendix, and Shi and Wang [16]), we obtain the main result of this section on the global bifurcations of steady state solutions: Theorem 3.”
• Stability, Steady‐State Bifurcations, and Turing Patterns in a Predator–Prey Model with Herd Behavior and Prey‐taxis (2017, methodology): “Thus, we can see that operator (27) is elliptic; moreover, it is strongly elliptic and satisfies the Agmon’s condition for angles θ ∈ [−π2 , π2 ] according to case 2 with N = 1 of remark 2.5.5 in Shi and Wang [46].”
• Global bifurcation analysis and pattern formation in homogeneous diffusive predator–prey systems (2016, methodology): “Indeed to obtain the four alternatives stated here, we have to use a more general version of global bifurcation theorem restricted to the positive cone in the function space, which is similar to the corresponding result in [38] for steady state solutions.”
• Pattern Formation of the Attraction-Repulsion Keller-Segel System (2013, neutral): “Recently a global bifurcation analysis for steady states was carried out in [53] for a class of regularized models of the classical KellerSegel models surveyed in [16], see also related work in [44, 51, 52].”
• Dynamics of a host-pathogen system on a bounded spatial domain (2015, methodology): “We apply a global bifurcation theorem in [28] to consider the solutions of (3.”
• Strong Allee effect in a diffusive predator–prey system with a protection zone☆ (2014, background): “(iii) The existence of the connected components S1 and S2 follows from the global bifurcation theorem in [47] or [45], and it is known that i = 1,2, Si is either unbounded, or it connects to another (d,ui,0) (where u1 = 1 and u2 = b), or Si connects to another point on the boundary of S .”
• Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, background): “For a treatment of global bifurcation as it applies to the quasilinear elliptic systems that describe equilibria of models for interacting species with cross diffusion or other forms of density-dependent diffusion or advection, see [78] and the references in that paper.”