Existence and multiplicity of solutions to triharmonic problems

The authors consider the triharmonic equation $$ (-\Delta)^3u+c_1\Delta^2 u+c_2\Delta u=h(x)|u|^{p-2} u+g(x,u)$$ in \(\Omega\), where \(p\in(1,2)\), subject to Navier boundary conditions. Based on the least action principle, the Ekeland's variational principle and a variant version of mountain pass lemma, we analyze the existence and multiplicity of nontrivial solutions to the above problem. In addition, we obtain the first eigenvalue of triharmonic operator and consider its structure. The conclusions are illustrated with several examples. For more information see https://ejde.math.txstate.edu/Volumes/2025/86/abstr.html