Nodal solutions for the weighted biharmonic equation with critical exponential growth

Brahim Dridi; Rachaid Jaidane

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arXiv · 2206.10001

Nodal solutions for the weighted biharmonic equation with critical exponential growth

Brahim Dridi·Rachaid Jaidane

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Abstract

In this paper, we deal with the logarithmic weighted fourth order elliptic equation in the unit disk of $B\subset\R^{4}$: $$\displaystyle(P_{\lambda})~~\Delta(w(x) \Delta u) = \lambda\ f(x,u) \quad\mbox{ in }\quad B, \quad u=\frac{\partial u}{\partial n} \quad\mbox{ on } \quad\partial B,$$ where the nonlinearity $f$ is assumed to have exponential critical growth in view of Adam's type inequalities. By using the constrained minimization in Nehari set combined with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions to the problem $(P_{\lambda})$ .

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Brahim Dridi, Rachaid Jaidane. 2022-06-20. Nodal solutions for the weighted biharmonic equation with critical exponential growth. https://arxiv.org/abs/2206.10001

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