Existence of saddle solutions of a nonlinear elliptic equation involving p-Laplacian in more even-dimensional spaces

Abstract

We show that there exist saddle solutions of the nonlinear elliptic equation involving the p-Laplacian, p>2, -{{\displaystyle \Delta }}_{p}u=f(u) in {ℝ}^{\mathrm{2}m} for all dimensions satisfying 2m≥p, by using sub-supersolution method. The existence of saddle solutions of the above problem was known only in dimensions 2m≥2p.

Key words： p-Laplacian; saddle solutions; sub-supersolution method

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