Existence of solutions for quasilinear elliptic boundary value problems in unbounded domains.
Existence of solutions for quasilinear parabolic equations with nonlocal boundary conditions.
Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than 8π as the initial data is given. This result was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.
Existence of solutions to a phase-field model with phase-dependent heat absorption.
Existence of solutions to a superlinear -Laplacian equation.
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...
Existence of solutions to -Laplace equations with logarithmic nonlinearity.
Existence of solutions to singular elliptic equations with convection terms via the Galerkin method.
Existence of solutions to the Rosenau and Benjamin-Bona-Mahony equation in domains with moving boundary.
Existence of solutions to the (rot,div)-system in -weighted spaces
The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, , S = ∂Ω in weighted -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.
Existence of stable periodic solutions for quasilinear parabolic problems in the presence of well-ordered lower and upper-solutions.
Existence of stable periodic solutions of a semilinear parabolic problem under Hammerstein-type conditions.
Existence of strong solutions for a class of nonlinear partial differential equations satisfying nonlinear boundary conditions
Existence of three solutions for a class of (p₁,...,pₙ)-biharmonic systems with Navier boundary conditions
We establish the existence of at least three weak solutions for the (p1,…,pₙ)-biharmonic system ⎧ in Ω, ⎨ ⎩ on ∂Ω, for 1 ≤ i ≤ n. The proof is based on a recent three critical points theorem.
Existence of threedimensional, steady, inviscid, incompressible flows with nonvanishing vorticity.
Existence of time periodic solutions for one-dimensional Newtonian filtration equation with multiple delays.
Existence of time-periodic solutions to incompressible Navier-Stokes equations in the whole space.
Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent
We study the following singular elliptic equation with critical exponent ⎧ in Ω, ⎨u > 0 in Ω, ⎩u = 0 on ∂Ω, where (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.
Existence of unstable sets for invariant sets in compact semiflows. Applications in order-preserving semiflows