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In this paper, we establish existence results and energy estimatesof weak solutions for an equation involving a $p$-harmonic operator, subject toDirichlet boundary conditions in a bounded smooth open domain of $\mathbb{R}^N$. A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least one non-trivial weak solution.

NON-TRIVIAL SOLUTIONS FOR $p$-HARMONIC TYPE EQUATIONS VIA A LOCAL MINIMUM THEOREM FOR FUNCTIONALS