caa a22 4500 605496501 CHVBK 20210128100536.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10231-014-0428-0 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0428-0 Teng Kaimin Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, People's Republic of China aut Two nontrivial solutions for an elliptic problem involving some nonlocal integro-differential operators [Elektronische Daten] [Kaimin Teng] In this paper, we show the existence of at least two nontrivial solutions of the nonlinear elliptic problem driven by nonlocal integro-differential operators $$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} \mathcal {L}_Ku=\lambda f(x,u), &{} \hbox {in } \Omega , \\ u=0, &{} \hbox {on } \mathbb {R}^N\backslash \Omega , \end{array} \right. \end{aligned}$$ L K u = λ f ( x , u ) , in Ω , u = 0 , on R N \ Ω , where $$\lambda \in \mathbb {R}$$ λ ∈ R is a parameter and $$\begin{aligned} \mathcal {L}_Ku(x)=2\mathrm{P.V. }\int \limits _{\mathbb {R}^N}|u(x)-u(y) |^{p-2}(u(x)-u(y))K(x-y)\hbox {d}y \end{aligned}$$ L K u ( x ) = 2 P . V . ∫ R N | u ( x ) - u ( y ) | p - 2 ( u ( x ) - u ( y ) ) K ( x - y ) d y and $$K$$ K belongs to a class of singular symmetric kernels modeled on the case $$K(x,y)=|x-y|^{-(N+sp)},\, \mathrm{P.V. }$$ K ( x , y ) = | x - y | - ( N + s p ) , P . V . is a commonly used abbreviation for in the principal value sense. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Fractional p -Laplacian nationallicence Nonlocal operators nationallicence Variational methods nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1455-1468 0373-3114 194:5<1455 2015 194 10231 https://doi.org/10.1007/s10231-014-0428-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0428-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Teng Kaimin Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, People's Republic of China aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/5(2015-10-01), 1455-1468 0373-3114 194:5<1455 2015 194 10231