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Solutions to semilinear p-Laplacian Dirichlet problem in population dynamics

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Abstract

In this article, we study a semilinear p-Laplacian Dirichlet problem arising in population dynamics. We obtain the Morse critical groups at zero. The results show that the energy functional of the problem is trivial. As a consequence, the existence and bifurcation of the nontrivial solutions to the problem are established.

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References

  1. Namba, T. Dencity-dependent dispersal and spatial distribution of a population. J. Theoret. Biol. 86(2), 351–363 (1980)

    Article  MathSciNet  Google Scholar 

  2. Carriao, P. and Miyagaki, O. Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems. J. Math. Anal. Appl. 230(1), 157–172 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  3. Hahan, W. Stability of Monoton, Springer-Verlag, Berlin / New York (1967)

    Google Scholar 

  4. Alama, S. Semilinear elliptic equations with sublinear indefinite nonlinearities. Adv. Differ. Equations 4(6), 813–842 (1999)

    MATH  MathSciNet  Google Scholar 

  5. Bartsch, T. and Wang, Z. Q. On the existence of sing changing solutions for semilinear Dirichlet problems. Topol. Methods Nonlinear Anal. 7(1), 115–131 (1996)

    MATH  MathSciNet  Google Scholar 

  6. Dancer, E. N. and Du, Y. The generalized Conley index and multiple solutions of semilinear elliptic problems. Abstr. Appl. Anal. 1(1), 103–135 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Moroz, V. On the Morse critical groups for infinite sublinear elliptic problems. Nonlinear Anal. 52(5), 1441–1453 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Perera, K. Nontrivial critical groups in p-Laplacian problems via the Yang index. Topol. Methods Nonlinear Anal. 21(2), 301–309, (2003)

    MATH  MathSciNet  Google Scholar 

  9. Mawhin, J. and Willem, M. Critical Point Theory and Hamiltonian Systems, Springer, Berlin (1989)

    MATH  Google Scholar 

  10. Chang, K. C. Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston (1993)

    MATH  Google Scholar 

  11. Jiu, Q. and Su, J. Existence and multiplicity results for Dirichlet problems with p-Laplacian. J. Math. Anal. Appl. 281(2), 587–601 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Dicle University, Diyarbakir, 21280, Turkey

    R. A. Mashiyev & S. Ogras

  2. Department of Mathematical Sciences, Inonu University, Malatya, 44280, Turkey

    G. Alisoy

Authors
  1. R. A. Mashiyev
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  2. G. Alisoy
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  3. S. Ogras
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Correspondence to R. A. Mashiyev.

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Communicated by Li-qun CHEN

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Mashiyev, R.A., Alisoy, G. & Ogras, S. Solutions to semilinear p-Laplacian Dirichlet problem in population dynamics. Appl. Math. Mech.-Engl. Ed. 31, 247–254 (2010). https://doi.org/10.1007/s10483-010-0212-6

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  • DOI: https://doi.org/10.1007/s10483-010-0212-6

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