Two nontrivial solutions for an elliptic problem involving some nonlocal integro-differential operators
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| 003 | CHVBK | ||
| 005 | 20210128100536.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20151001xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10231-014-0428-0 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-014-0428-0 | ||
| 100 | 1 | |a Teng |D Kaimin |u Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, People's Republic of China |4 aut | |
| 245 | 1 | 0 | |a Two nontrivial solutions for an elliptic problem involving some nonlocal integro-differential operators |h [Elektronische Daten] |c [Kaimin Teng] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 | ||
| 690 | 7 | |a Fractional p -Laplacian |2 nationallicence | |
| 690 | 7 | |a Nonlocal operators |2 nationallicence | |
| 690 | 7 | |a Variational methods |2 nationallicence | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1455-1468 |x 0373-3114 |q 194:5<1455 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-014-0428-0 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-014-0428-0 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Teng |D Kaimin |u Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi, People's Republic of China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/5(2015-10-01), 1455-1468 |x 0373-3114 |q 194:5<1455 |1 2015 |2 194 |o 10231 | ||