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Infinitely many small energy solutions for equations involving the fractional Laplacian in $\mathbb R^{N}$

김연호
대한수학회 (The Korean Mathematical Society)|2018.09|대한수학회지 (Journal of the KMS)|제55권 제5호|pp. 1269-1283

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참고문헌

키워드

variational methodsfractional Laplacianintegrodifferential operatorsinfinitely many solutions
주제분류수학

초록

We are concerned with elliptic equations in $\mathbb R^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to $0$ in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

Abstract

We are concerned with elliptic equations in $\mathbb R^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to $0$ in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

참고문헌 (36)

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