Abstract
In this paper, we are concerned with the existence of least energy sign-changing solutions for the following N-Laplacian Kirchhoff-type problem with logarithmic and exponential nonlinearities:
where f(t) behaves like \(\ exp\left( {\alpha |t|^{{\frac{N}{{N - 1}}}} } \right) \). Combining constrained variational method, topological degree theory and quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution \(u_{b}\) with precisely two nodal domains. Moreover, we show that the energy of \(u_{b}\) is strictly larger than two times of the ground state energy and analyze the convergence property of \(u_{b}\) as \(b\searrow 0\).
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This study was supported in part by grants from National Natural Science Foundation of China (No. 12271443)
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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [TH]and [Y-YS]. The first draft of the manuscript was written by [TH] and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Huang, T., Shang, YY. Least Energy Sign-Changing Solution for N-Kirchhoff Problems with Logarithmic and Exponential Nonlinearities. Complex Anal. Oper. Theory 18, 49 (2024). https://doi.org/10.1007/s11785-024-01495-4
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DOI: https://doi.org/10.1007/s11785-024-01495-4
Keywords
- N-Laplacian Kirchhoff-type equation
- Logarithmic nonlinearity
- Exponential growth
- Sign-changing solutions