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• W2301864576 abstract "In this paper, we prove the existence of infinitely many nontrivial solutions of the following equations driven by a nonlocal integro-differential operator $mathcal{L}_K$ with concave-convex nonlinearities and homogeneous Dirichlet boundary conditions begin{align*} mathcal{L}_{K} u + mu |u|^{q-1}u + lambda |u|^{p-1}u &= 0 quadmbox{in}quad Omega, u&=0 quadmbox{in}quadmathbb{R}^NsetminusOmega, end{align*} where $Omega$ is a smooth bounded domain in $ mathbb R^N $, $N > 2s$, $sin(0, 1)$, $0 < q < 1 < pleq frac{N+2s}{N-2s}$. Moreover, when $mathcal{L}_K$ reduces to the fractional laplacian operator $-(-Delta)^s $, $p=frac{N+2s}{N-2s}$, $frac{1}{2} (frac{N+2s}{N-2s}) < q < 1$, $N > 6s$, $ lambda =1$, we find $mu^*>0$ such that for any $muin(0,mu^*)$, there exists at least one sign changing solution." @default.
• W2301864576 created "2016-06-24" @default.
• W2301864576 creator A5044266541 @default.
• W2301864576 creator A5081222835 @default.
• W2301864576 date "2017-05-01" @default.
• W2301864576 modified "2023-09-26" @default.
• W2301864576 title "Multiplicity results and sign changing solutions of non-local equations with concave-convex nonlinearities" @default.
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• W2301864576 doi "https://doi.org/10.57262/die/1489802419" @default.
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