相关论文: Existence and multiplicity of solutions for a Diri…
The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…
We investigate the existence, non-existence, uniqueness, and multiplicity of positive solutions to the following problem: \begin{align}\label{P} \left\{ \begin{array}{l} D_{0+}^\alpha u + h(t)f(u) = 0, \quad 0<t<1, \\[1ex] u(0)=u(1)=0,…
We prove the existence and uniqueness of solutions to a Dirichlet problem \[ \begin{cases} Lu = f + v^{-1}\text{Div}(v{\bf e} h), & x \in \Omega; u = 0, & x \in \partial \Omega, \end{cases}\] where $L$ is a degenerate, linear, second order…
We prove the existence of at least three solutions for a weighted $p$-Laplacian operator involving Dirichlet boundary condition in a weighted Sobolev space. The main tool we use here is a three solution theorem in reflexive Banach spaces…
In this paper we prove the existence and uniqueness of positive classical solution of the fractional Laplacian with singular nonlinearity in a smooth bounded domain with zero Drichlet boundary conditions. By the method of sub-supersolution,…
We establish interior and up to the boundary H\"older regularity estimates for weak solutions of the Dirichlet problem for the fractional $g-$Laplacian with bounded right hand side and $g$ convex. These are the first regularity results…
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear…
In this paper we investigate the existence of multiple solutions for the following two fractional problems \begin{equation*} \left\{\begin{array}{ll} (-\Delta_{\Omega})^{s} u-\lambda u= f(x, u) &\mbox{in} \Omega \\ u=0 &\mbox{in} \partial…
The existence of positive, pointwise decaying at infinity, weak solutions to a fractional $p$-Laplacian problem in the whole space and with singular reaction is established. Truncation arguments, variational methods, as well as suitable a…
This study investigates Dirichlet boundary condition related to a class of nonlinear parabolic problem with nonnegative $L^1$-data, which has a variable-order fractional $p$-Laplacian operator. The existence and uniqueness of renormalized…
We study sharp conditions for the existence and nonexistence of infinitely many nonnegative solutions to the problem $-\Delta_p u = \lambda f(u)$ in a bounded domain with Dirichlet boundary conditions, where $f$ is a continuous function…
We study the eigenvalue problem for the $g-$Laplacian operator in fractional order Orlicz-Sobolev spaces, where $g=G'$ and neither $G$ nor its conjugated function satisfy the $\Delta_2$ condition. Our main result is the existence of a…
This paper is devoted to study the existence and multiplicity solutions for the nonlinear Schr\"odinger-Poisson systems involving fractional Laplacian operator: \begin{equation}\label{eq*} \left\{ \aligned &(-\Delta)^{s} u+V(x)u+ \phi…
We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction term which is resonant at infinity between two non-principal eigenvalues: for such equation…
In this paper, we obtain nonexistence results of positive solutions, and also the existence of an unbounded sequence of solutions that changing sign for some critical problems involving conformally invariant operators on the standard unit…
In this article, we investigate the existence and uniqueness of a positive solution for a class of singular nonlinear elliptic problem with boundary condition. Our result holds in fractional Orlicz-Sobolev spaces.
We study a nonlinear, nonlocal Dirichlet problem driven by the fractional p-Laplacian, involving a (p-1)-sublinear reaction. By means of a weak comparison principle we prove uniqueness of the solution. Also, comparing the problem to…
We study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional Laplacian: (-\Delta)^{\alpha/2}u=\lambda u^q+u^{\frac{N+\alpha}{N-\alpha}}, \quad…
The existence of at least two solutions to superlinear integral equation in cone is proved using the Krasnosielskii Fixed Point Theorem. The result is applied to the Dirichlet BVPs with the fractional Laplacian.
We present a result of existence of infinitely many solutions for the Dirichlet problem involving the p-Laplacian in annular domains, when $p\leq N$, contouring the failure of compactness of $W^{1,p}(\Omega)$ in $C^0(\bar{\Omega})$ applying…