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

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  • Ronaldo C. Duarte

    (Universidade Federal do Rio Grande do Norte)

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.

Suggested Citation

  • Ronaldo C. Duarte, 2022. "Ground state solution for nonlocal scalar field equations involving an integro-differential operator," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-14, April.
    • Handle: RePEc:spr:pardea:v:3:y:2022:i:2:d:10.1007_s42985-022-00156-5
    DOI: 10.1007/s42985-022-00156-5
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    References listed on IDEAS

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    1. Frank H. Clarke, 1976. "A New Approach to Lagrange Multipliers," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 165-174, May.
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