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Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity

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  • Ayékotan Messan Joseph Tchalla
  • Kokou Tcharie
  • Nawab Hussain

Abstract

This paper deals with the existence of weak solutions to a Dirichlet problem for a semilinear elliptic equation involving the difference of two main nonlinearities functions that depends on a real parameter λ. According to the values of λ, we give both nonexistence and multiplicity results by using variational methods. In particular, we first exhibit a critical positive value such that the problem admits at least a nontrivial non-negative weak solution if and only if λ is greater than or equal to this critical value. Furthermore, for λ greater than a second critical positive value, we show the existence of two independent nontrivial non-negative weak solutions to the problem.

Suggested Citation

  • Ayékotan Messan Joseph Tchalla & Kokou Tcharie & Nawab Hussain, 2022. "Multiplicity Results for Weak Solutions of a Semilinear Dirichlet Elliptic Problem with a Parametric Nonlinearity," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-19, November.
    • Handle: RePEc:hin:jijmms:6011860
    DOI: 10.1155/2022/6011860
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