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arXiv · 2410.00189

Nonlinear scalar field equation with point interaction

Alessio Pomponio·Tatsuya Watanabe
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Abstract

This paper is devoted to the study of the nonlinear scalar field equation with a point interaction at the origin in dimensions two and three. By applying the mountain pass theorem and the technique of adding one dimensional space, we prove the existence of a nontrivial singular solution for a wide class of nonlinearities. We also establish the Pohozaev identity by proving a pointwise estimate of the gradient near the origin. Some qualitative properties of nontrivial solutions are also given.

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Alessio Pomponio, Tatsuya Watanabe. 2024-09-30. Nonlinear scalar field equation with point interaction. https://doi.org/10.1137/24m1700892

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