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EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRODINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN R-N
- EXISTENCE OF WEAK SOLUTIONS TO A CLASS OF SCHRODINGER TYPE EQUATIONS INVOLVING THE FRACTIONAL p-LAPLACIAN IN R-N
- Kim, Jae-Myoung; Kim, Yun-Ho; Lee, Jongrak
- Ewha Authors
- Issue Date
- Journal Title
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
- JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY vol. 56, no. 6, pp. 1529 - 1560
- fractional p-Laplacian; variational methods; critical point theory
- KOREAN MATHEMATICAL SOC
- SCIE; SCOPUS; KCI
- Document Type
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- We are concerned with the following elliptic equations: (-Delta)(p)(s)u + V(x)vertical bar u vertical bar(p-2)u = lambda g(x,u) in R-N, where (-Delta)(p)(s) is the fractional p-Laplacian operator with 0 < s < 1 < p < + infinity, sp < N, the potential function V : R-N -> (0, infinity) is a continuous potential function, and g : R-N x R -> R satisfies a Caratheodory condition. We show the existence of at least one weak solution for the problem above without the Ambrosetti and Rabinowitz condition. Moreover, we give a positive interval of the parameter lambda for which the problem admits at least one nontrivial weak solution when the nonlinearity g has the subcritical growth condition.
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