Existence of positive entire solutions of semilinear elliptic equations on .
Existence of positive solutions for nonlinear boundary value problems in bounded domains of .
Existence of positive solutions for some nonlinear elliptic problems in unbounded domains of .
Existence of positive solutions for some polyharmonic nonlinear equations in .
Existence of positive solutions to a superlinear elliptic problem.
Existence of pseudo almost automorphic solutions for the heat equation with -pseudo almost automorphic coefficients.
Existence of pseudo-almost automorphic mild solutions to some nonautonomous partial evolution equations.
Existence of renormalized solutions for parabolic equations without the sign condition and with three unbounded nonlinearities
We study the problem ∂b(x,u)/∂t - div(a(x,t,u,Du)) + H(x,t,u,Du) = μ in Q = Ω×(0,T), in Ω, u = 0 in ∂Ω × (0,T). The main contribution of our work is to prove the existence of a renormalized solution without the sign condition or the coercivity condition on H(x,t,u,Du). The critical growth condition on H is only with respect to Du and not with respect to u. The datum μ is assumed to be in and b(x,u₀) ∈ L¹(Ω).
Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations
We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.
Existence of solutions for a nonlinear elliptic equation with general flux term.
Existence of solutions for a sublinear system of elliptic equations.
Existence of solutions for a system of elliptic partial differential equations.
Existence of solutions for elliptic systems with nonlocal terms in one dimension.
Existence of solutions for fourth-order PDEs with variable exponents.
Existence of solutions for non-linear systems of differential-functional equations of parabolic type in an arbitrary domain
Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.
Existence of solutions for some quasi-variational inequalities
Existence of solutions for two types of generalized versions of the Cahn-Hilliard equation
We show existence of solutions to two types of generalized anisotropic Cahn-Hilliard problems: In the first case, we assume the mobility to be dependent on the concentration and its gradient, where the system is supplied with dynamic boundary conditions. In the second case, we deal with classical no-flux boundary conditions where the mobility depends on concentration , gradient of concentration and the chemical potential . The existence is shown using a newly developed generalization of gradient...
Existence of solutions to microhyperbolic boundary value problems
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...