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

Ayékotan Messan Joseph Tchalla, Kokou Tcharie and Nawab Hussain

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-19

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:6011860

DOI: 10.1155/2022/6011860

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