A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem
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Publication:543918
DOI10.1016/J.JDE.2011.03.017zbMath1229.34037OpenAlexW2020740704MaRDI QIDQ543918
Publication date: 17 June 2011
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2011.03.017
positive solutionexact multiplicityS-shaped bifurcation curvepositone problemconvex-concave nonlinearityperturbed Gelfand problem
Bifurcation theory for ordinary differential equations (34C23) Multiplicity of solutions of equilibrium problems in solid mechanics (74G35) Positive solutions to nonlinear boundary value problems for ordinary differential equations (34B18)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the structure of solutions of an equation in catalysis theory when a parameter is large
- Computing the location and the direction of bifurcation
- Numerical method for verifying the existence and local uniqueness of a double turning point for a radially symmetric solution of the perturbed Gelfand equation
- Remarks on an S-shaped bifurcation curve
- Global bifurcation of steady-state solutions
- Mathematical problems from combustion theory
- Persistence and bifurcation of degenerate solutions
- Non-simple Turning Points and Cusps
- The number of solutions to an equation from catalysis
- S-shaped bifurcation curves
- On the exactness of an S-shaped bifurcation curve
- On s-shaped bifurcation curves
- Proof of a conjecture for the perturbed Gelfand equation from combustion theory
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