Abstract
We investigate the degenerate bi-harmonic equation
with \(m\ge 2\), and also the degenerate tri-harmonic equation:
where \(\Omega\subset \mathbb{R}^{N}\) is a bounded domain with smooth boundary \(N>4\) or \(N>6\) respectively, and \(f \in \mathrm{C}^{1}(\Omega\times \mathbb{R})\) satisfies suitable m-superlinear and subcritical growth conditions. Our main purpose is to establish \(L^{p}\) and \(L^{\infty}\) explicit bounds for weak solutions via the Morse index. Our results extend previous explicit estimates obtained in [1]–[4].
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References
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Funding
The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, KSA, for funding this work through Research Group under grant number (R.G.P-2/121/42).
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Mtiri, F. Solutions of Super-Linear Elliptic Equations and Their Morse Indices. Math Notes 109, 759–776 (2021). https://doi.org/10.1134/S0001434621050096
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DOI: https://doi.org/10.1134/S0001434621050096