Existence of solutions for the surface electromigration equation

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Qualitative Properties and Existence of Solutions for a Generalized Fisher-like Equation

This paper is devoted to the study of an eigenvalue second order differential equation, supplied with homogenous Dirichlet conditions and set on the real line. In the linear case, the equation arises in the study of a reaction-diffusion system involved in disease propagation throughout a given population. Under some relations upon the real parameters and coefficients, we present some existence ...

Existence and Regularity of Weak Solutions to the Prescribed Mean Curvature Equation for a Nonparametric Surface

It is known that for the parametric Plateau’s problem, weak solutions can be obtained as critical points of a functional (see [2, 6, 7, 8, 10, 11]). The nonparametric case has been studied for H = H(x,y) (and generally H = H(x1, . . . ,xn) for hypersurfaces in Rn+1) by Gilbarg, Trudinger, Simon, and Serrin, among other authors. It has been proved [5] that there exists a solution for any smooth ...

Global Existence of Weak Solutions for the Burgers-Hilbert Equation

This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in L(IR). For positive times, the solution lies in L2∩L∞. A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.

Existence of Periodic Solutions for the Duffing Equation with Impulses