On fractional p-Laplacian problems with local conditions

Abstract

In this paper, we deal with fractional p-Laplacian equations of the form\left\{\begin{aligned} \displaystyle(-\Delta)_{p}^{s}u&\displaystyle=\lambda f% (x,u),&&\displaystyle x\in\Omega,\\ \displaystyle u(x)&\displaystyle=0,&&\displaystyle x\in\mathbb{R}^{N}\setminus% \Omega,\end{aligned}\right.where {\lambda\in(0,+\infty)}, {0<s<1<p<+\infty} and {\Omega\subset\mathbb{R}^{N}}, {N\geqslant 2}, is a bounded domain with smooth boundary. With assumptions on {f(x,t)} just in {\Omega\times(-\delta,\delta)}, where {\delta>0} is small, existence and multiplicity of nontrivial solutions are obtained via variational methods.

Neumann fractionalp-Laplacian: Eigenvalues and existence results

“…See [12] and [29] for other general conditions on f which imply the Ambrosetti-Rabinowitz one, and [17] for other related conditions. Now we are ready to give the definition of a weak solution of our problem.…”

Multiple positive solutions for mixed fractional differential system with p-Laplacian operators

“…Fractional differential equation with p-Laplacian operator can describe the nonlinear phenomena in non-Newtonian fluids and establishes complex process models; for some related articles, see [25][26][27][28][29][30][31]. Via variational methods, Li and Wei [32] dealt with fractional p-Laplacian equations, the existence and multiplicity of nontrivial solutions were obtained. Wu et al [33] researched the following fractional differential turbulent flow model and obtained the iterative solutions of the equation:…”

Monotone iterative method for a p-Laplacian boundary value problem with fractional conformable derivatives

“…Fractional p-Laplacian boundary value problems also received considerable attention, for example, see [16][17][18][19][20][21][22][23][24][25][26]. The literature on fractional differential equations equipped with integral boundary conditions also contains a variety of interesting results [27][28][29][30][31][32].…”