caa a22 4500 606244603 CHVBK 20210128101331.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s12044-015-0244-5 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0244-5 Nehari manifold for non-local elliptic operator with concave-convex nonlinearities and sign-changing weight functions [Elektronische Daten] [SARIKA GOYAL, K SREENADH] In this article, we study the existence and multiplicity of non-negative solutions of the following p-fractional equation: − 2 ∫ ℝ n | u ( y ) − u ( x ) | p − 2 ( u ( y ) − u ( x ) ) | x − y | n + pα d y = λh ( x ) | u | q − 1 u + b ( x ) | u | r − 1 u in Ω , u = 0 in ℝ n ∖ Ω , u ∈ W α , p ( ℝ n ) $$\quad \left\{ \begin{array}{lr}\displaystyle \!\! - 2{\int}_{\mathbb R^{n}}\!\frac{|u(y)-u(x)|^{p-2}(u(y)\,-\,u(x))}{|x-y|^{n+p\alpha}}\mathrm{d}y = \lambda h(x)|u|^{q-1}u\,+\, b(x)|u|^{r-1} u \; \text{in}\; {\Omega}, \\ \quad \quad\quad \quad\quad u =0\quad\quad \text{in}\;\mathbb{R}^{n}\setminus {\Omega},\quad u\in W^{\alpha,p}(\mathbb R^{n}) \end{array} \right. $$ where Ω is a bounded domain in ℝ n $\mathbb R^{n}$ with continuous boundary, p ≥ 2, n > p α, α ∈ (0, 1), 0 < q < p −1 < r < p ∗ − 1 with p ∗ = np(n − p α)−1, λ > 0 and h, b are sign-changing continuous functions. We show the existence and multiplicity of solutions by minimization on the suitable subset of Nehari manifold using the fibering maps. We find that there exists λ 0 such that for λ ∈ (0, λ 0), it has at least two non-negative solutions. Indian Academy of Sciences, 2015 Non-local operator nationallicence p -fractional Laplacian nationallicence sign-changing weight functions nationallicence Nehari manifold nationallicence fibering maps nationallicence GOYAL SARIKA Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, 110 016, New Delhi, India aut SREENADH K. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, 110 016, New Delhi, India aut Proceedings - Mathematical Sciences Springer India 125/4(2015-11-01), 545-558 0253-4142 125:4<545 2015 125 12044 https://doi.org/10.1007/s12044-015-0244-5 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/s12044-015-0244-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- GOYAL SARIKA Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, 110 016, New Delhi, India aut NATIONALLICENCE 700 1- SREENADH K. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, 110 016, New Delhi, India aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/4(2015-11-01), 545-558 0253-4142 125:4<545 2015 125 12044