Ground state solution for nonlocal scalar field equations involving an integro-differential operator

Ronaldo C. Duarte ()
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Ronaldo C. Duarte: Universidade Federal do Rio Grande do Norte

Partial Differential Equations and Applications, 2022, vol. 3, issue 2, 1-14

Abstract: Abstract This paper is concerned with nonlocal scalar field equations involving an integro-differential operator. We investigate the existence of solutions for the problem $$\begin{aligned} -\mathcal {L}_{K}u=g(u) \end{aligned}$$ - L K u = g ( u ) in $$\mathbb {R}^N$$ R N , where $$-\mathcal {L}_{K}$$ - L K is an integro-differential operator. Under appropriate hypotheses, we prove that this equation has a ground state solution.

Keywords: Integro-differential; Polya–Szego inequality; Scalar field equations; Primary 35J20; Secondary 35A15; 35J60 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00156-5

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