0 is a bifurcation parameter and c>0 is an evolution parameter. We mainly prove that, under some suitable assumptions on f, there exists c₁>0, such that, on the (λ,‖u‖∞)-plane, (i) when 0 Airiti Library
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Reference ( 11 ) 〈TOP〉
  1. Drame-Costa : A.K. Drame, D.G. Costa, On positive solutions of one-dimensional semipositone equations with nonlinear boundary conditions, Appl. Math. Lett. 25 (2012) 2411--2416.
  2. Goddard-Shivaji-Lee : J. Goddard II, R. Shivaji, E.K. Lee, A double S-shaped bifurcation curve for a reaction-diffusion model with nonlinear boundary conditions, Bound. Value Probl. 2010, Art. ID 357542, 23 pages.
  3. Gordon-Ko-Shivaji : P.V. Gordon, E. Ko, R. Shivaji, Multiplicity and uniqueness of positive solutions for elliptic equations with nonlinear boundary conditions arising in a theory of thermal explosion, Nonlinear Anal.: Real World Appl. 15 (2014) 51--57.
  4. Huang-Wang1 : S.-Y. Huang, S.-H. Wang, Proof of a conjecture for the one-dimensional perturbed Gelfand problem from combustion theory, Arch. Rational Mech. Anal. (2016) 1--57. (DOI) 10.1007/s00205-016-1011-1
  5. Hung-Wang1 : K.-C. Hung, S.-H. Wang, A theorem on S-shaped bifurcation curve for a positone problem with convex-concave nonlinearity and its applications to the perturbed Gelfand problem, J. Differential Equations 251 (2011) 223--237.
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