TY - JOUR
T1 - On the existence of positive solutions to a certain class of semilinear elliptic equations
AU - Ikoma, Norihisa
N1 - Funding Information:
The author would like to thank Lawrence Craig Evans for pointing out the variational structure of () to him. He also would like to thank Hitoshi Ishii for helpful comments on the consideration of (). The author was supported by JSPS KAKENHI Grant Numbers JP 17H02851, 19H01797 and 19K03590.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
PY - 2021/4
Y1 - 2021/4
N2 - In this paper, we study the following semilinear elliptic equation Δu=φ(V(x)u-f(x,u(x)))inRN,u∈H1(RN)where N≥ 1 and φ(s) , V(x), f(x, s) are given functions. Under some conditions on φ(s) , V(x) , f(x, s) , we show the existence of positive solution. In particular, we extend the result of Felmer and Ikoma (J Funct Anal 275(8):2162–2196, 2018). In Felmer and Ikoma (J Funct Anal 275(8):2162–2196, 2018), the existence of positive solution was proved by topological degree theoretic argument. In this paper, we employ the variational method.
AB - In this paper, we study the following semilinear elliptic equation Δu=φ(V(x)u-f(x,u(x)))inRN,u∈H1(RN)where N≥ 1 and φ(s) , V(x), f(x, s) are given functions. Under some conditions on φ(s) , V(x) , f(x, s) , we show the existence of positive solution. In particular, we extend the result of Felmer and Ikoma (J Funct Anal 275(8):2162–2196, 2018). In Felmer and Ikoma (J Funct Anal 275(8):2162–2196, 2018), the existence of positive solution was proved by topological degree theoretic argument. In this paper, we employ the variational method.
KW - Concentration-compactness lemma
KW - Mountain pass theorem
KW - Positive solution
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U2 - 10.1007/s42985-021-00079-7
DO - 10.1007/s42985-021-00079-7
M3 - Article
AN - SCOPUS:85126327021
VL - 2
JO - Partial Differential Equations and Applications
JF - Partial Differential Equations and Applications
SN - 2662-2963
IS - 2
M1 - 28
ER -