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Exact multiplicity results for boundary value problems with nonlinearities generalising cubic

  • Philip Korman (a1), Yi Li (a2) and Tiancheng Ouyang (a3)
Abstract

Using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type

The first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u. The second one deals with a class of nonlinearities with explicit x dependence.

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3B. Gidas , W.-M. Ni and L. Nirenberg . Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68 (1979) 209–43.

5P. Korman and T. Ouyang . Multiplicity results for two classes of boundary-value problems. SIAM J. Math. Anal. 26 (1995), 180–9.

7H. Matano . Asymptotic behavior and stability of solutions of semilinear diffusion equations. Publ. RIMS, Kyoto Univ. 15 (1979) 401–54.

8P. H. Rabinowitz . Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics 65 (Providence, R.I.: American Mathematical Society, 1986).

10J. Smoller and A. Wasserman . Global bifurcation of steady-state solutions. J. Differential Equations 39(1981), 269–90.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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