Related papers: Existence and uniqueness for a class of nonlinear …
In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to the nonlinear fractional elliptic problem of type $(P)$ (see below) involving singular nonlinearity and singular weights in smooth…
We prove the existence of non-trivial solutions for a fractional Schr$\ddot{o}$dinger-Poisson equation in $\mathbb{R}^{3}$. The proof is based on the perturbation method and the mountain pass theorem.
In this paper we will discuss the Dirichlet problem of nonlinear second order partial differential equations resolved with any derivatives. First, we transform it into generalized integral equations. Next, we discuss the existence of the…
We study existence and uniqueness of solutions to a class of nonlinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To…
The aim of this paper is to obtain the existence of solutions for the following fractional p-Laplacian Dirichlet problem with mixed derivatives \begin{eqnarray*}…
We consider a strongly nonlinear differential equation of the following general type $$(\Phi(a(t,x(t)) \, x'(t)))'= f(t,x(t),x'(t)), \quad \text{a.e. on $[0,T]$}$$ where $f$ is a Carath\'edory function, $\Phi$ is a strictly increasing…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained…
We construct a theory of existence, uniqueness and regularity of solutions for the fractional heat equation $\partial_t u +(-\Delta)^s u=0$, $0<s<1$, posed in the whole space $\mathbb{R}^N$ with data in a class of locally bounded Radon…
In this note a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one-dimensional fractional problems admits at least one non-trivial solution under an asymptotical behaviour of the…
The purpose of this paper is to make a few connections among specific concepts occurring in differential geometry and the theory of differential equations with the aim of identifying an intriguing class of undetermined nonlinear ordinary…
We consider equations of the form $-L_\mu u +f(u)=0$ in a smooth domain $\Omega$, where $L_\mu=\Delta + \mu\delta^{-2}$ and $\delta(x)$ denotes the distance of the point $x$ to the boundary of the domain. The nonlinear term $f$ is positive,…
We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-\Delta)_{p(\cdot)}^{s}…
We prove the existence of periodic solutions in a class of nonlinear partial differential equations, including the nonlinear Schroedinger equation, the nonlinear wave equation, and the nonlinear beam equation, in higher dimension. Our…
We study the existence and nonexistence of positive singular solutions to second-order non-divergence type elliptic inequalities with measurable coefficients. We prove the existence of a critical value $p^*$ that separates the existence…
By means of two fractional order integral inequalities we investigate the existence and uniqueness of the solutions of the fractional nonlinear Volterra integral equation and a fractional nonlinear integrodifferential equation in Banach…
In this paper, we give a full classification of the nonexistence of positive weak solutions to the semilinear elliptic inequality involving the fractional Hardy potential in punctured and in exterior domains. Our methods are self-contained…
We consider fractional differential equations of order $\alpha \in (0,1)$ for functions of one independent variable $t\in (0,\infty)$ with the Riemann-Liouville and Caputo-Dzhrbashyan fractional derivatives. A precise estimate for the order…
In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\"odinger-Poisson equations in $\mathbb R^3$ with general nonlinearities.
In this article we have studied complex linear homogeneous difference equations where the coefficients are meromorphic functions, having finite iterated p-phi order. We have made some estimations on the growth of its nontrivial solutions.…