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Nodal solutions for logarithmic weighted N-laplacian problem with exponential nonlinearities

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Abstract

In this article, we study the following problem

$$\begin{aligned} -div (\omega (x)|\nabla u|^{N-2} \nabla u) = \lambda \ f(x,u) \quad \text{ in } \quad B, \quad u=0 \quad \text{ on } \quad \partial B, \end{aligned}$$

where B is the unit ball in \(\mathbb {R^{N}}\), \(N\ge 2\) and w(x) a singular weight of logarithm type. The reaction source f(x, u) is a radial function with respect to x and is subcritical or critical with respect to a maximal growth of exponential type. By using the constrained minimization in Nehari set coupled with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions.

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Authors and Affiliations

  1. Department of mathematics, Faculty of Applied Sciences, Umm Al-Qura University, P.O. Box 14035, Mecca, 21955, Saudi Arabia

    Brahim Dridi

  2. Department of Mathematics, Faculty of Science of Tunis, University of Tunis El Manar, Tunis, Tunisia

    Rached Jaidane

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  1. Brahim Dridi
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  2. Rached Jaidane
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Correspondence to Brahim Dridi.

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Dridi, B., Jaidane, R. Nodal solutions for logarithmic weighted N-laplacian problem with exponential nonlinearities. Ann Univ Ferrara 70, 63–88 (2024). https://doi.org/10.1007/s11565-023-00457-6

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