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Sign-changing solutions for quasilinear elliptic equation with critical exponential growth

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Abstract

We study the existence, energy doubling property and asymptotic behavior of sign-changing solutions for N-Laplacian equation of Kirchhoff type

$$\begin{aligned} {\left\{ \begin{array}{ll} -(a+ b\int _{\Omega }|\nabla u|^{N}dx)\Delta _N u=|u|^{p-2}u\ln |u|^2+ \mu g(u),&{}\quad in~\Omega ,\\ u=0,&{}\quad on~\partial \Omega . \end{array}\right. } \end{aligned}$$

By constraint variational methods, we apply the constraint minimization arguments to establish the existence of sign-changing solutions and ground state solutions for above problem. Our results extend existing results to the N-Laplacian equation of Kirchhoff type with logarithmic and exponential nonlinearities.

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Acknowledgements

The author is very grateful to the Professor Yang for the answer to author’s questions.

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  1. School of Science, Nantong University, Nantong, 226019, Jiangsu, People’s Republic of China

    Huabo Zhang

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Zhang, H. Sign-changing solutions for quasilinear elliptic equation with critical exponential growth. J. Appl. Math. Comput. 69, 2595–2616 (2023). https://doi.org/10.1007/s12190-023-01849-9

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