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Analysis reports a new approach for mountain-pass solutions in Schrödinger equations, suggesting minimal conditions for equations with nonlinearity.
For a Kirchhoff type Schrödinger equation with general potential and nonlinearity , it is known that to get a solution by using mountain‐pass theorem (i.e., a mountain‐pass solution) for this kind of equation, is usually required to be supercubic in at infinity, and certain properties on are also needed. The aim of this paper is to provide a direct and simple way to find a mountain‐pass solution for this equation under the weakest possible conditions on and . In particular, we propose a new condition on which is possibly the weakest in comparison to previous studies. Moreover, the relation between the least energy solution and the mountain‐pass solution of the equation is also discussed.
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Zhang et al. (2025) studied this question.
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