In this paper, we study the existence of monotone positive solutions which converge to the equilibrium of a nonlinear difference equation. Recently, there has been a lot of interest in studying such solutions and the existence of some specific solutions see 1–20 . In 8 , Karakostas and Stević studied the boundedness, global attractivity, and oscillatory and asymptotic periodicity of the nonnega...

We study properties of the semilinear elliptic equation ∆u = 1 u on domains in R, with an eye toward nonnegative singular solutions as limits of positive smooth solutions. We prove the nonexistence of such solutions in low dimensions when we also require them to be stable for the corresponding variational problem. The problem of finding singular solutions is related to the general study of sing...

In this paper, we are mainly concerned with the physically interesting static Schr\"{o}dinger-Hartree-Maxwell type equations \begin{equation*} (-\Delta)^{s}u(x)=\left(\frac{1}{|x|^{\sigma}}\ast |u|^{p}\right)u^{q}(x) \,\,\,\,\,\,\,\,\,\,\,\, \text{in} \,\,\, \mathbb{R}^{n} \end{equation*} involving higher-order or fractional Laplacians, where $n\geq1$, $0<s:=m+\frac{\alpha}{2}<\frac{n}{2}$, $m\...

Abstract We study the nonlocal nonlinear problem $$\begin{aligned} \left\{ \begin{array}[c]{lll} (-\Delta )^s u = \lambda f(u) &amp;{} \text{ in } \Omega , \\ u=0&amp;{}\text{ on \mathbb {R}^N{\setminus }\Omega \quad (P_{\lambda }) \end{array} \right. \end{aligned}$$ <m...

This paper deals with the existence of positive solutions for some boundary value problems of the singular differential equations on the whole line. Our approach is based on the fixed point theorem and the monotone iterative technique. Without the assumption of the existence of lower and upper solutions, we obtain not only the existence of nonnegative solutions for the problems, but also establ...

The large time behaviour of nonnegative solutions to a quasilinear degenerate diffusion equation with a source term depending solely on the gradient is investigated. After a suitable rescaling of time, convergence to a unique profile is shown for global solutions. The proof relies on the halfrelaxed limits technique within the theory of viscosity solutions and on the construction of suitable su...

This paper investigates the existence of solutions for a class of variable exponent integrodifferential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies subp− − 1 growth condition or general growth condition, we give the existence of solutions and nonnegative solutions via Leray-Schauder degree at nonresonance, respectively. Moreo...