Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.
Existence of solutions for one-dimensional wave equations with nonlocal conditions.
Existence of solutions for -Laplacian equations.
Existence of solutions for quasilinear degenerate elliptic equations.
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 some elliptic problems with critical Sobolev exponents.
Let Ω be a bounded domain in Rn with n ≥ 3. In this paper we are concerned with the problem of finding u ∈ H01 (Ω) satisfying the nonlinear elliptic problemsΔu + |u|(n+2/n-2) + f(x) = 0 in Ω and u(x) = 0 on ∂Ω, andΔu + u + |u|(n+2/n-2) + f(x) = 0 in Ω and u(x) = 0 on ∂Ω, when of f ∈ L∞(Ω).
Existence of solutions for some nonlinear elliptic equations.
Existence of solutions for some quasilinear -elliptic problem with Hardy potential
We consider the anisotropic quasilinear elliptic Dirichlet problem where is an open bounded subset of containing the origin. We show the existence of entropy solution for this equation where the data is assumed to be in and is a positive constant.
Existence of solutions for some quasi-variational inequalities
Existence of solutions for systems of self-referred and hereditary differential equations.
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 for the one-phase and the multi-layer free-boundary problems with the -Laplacian operator.
Existence of solutions for the -Laplacian problem with singular term.
Existence of solutions for the two-dimensional stationary Euler system for ideal fluids with arbitrary force
Existence of solutions for thermoelastic semiconductor equations.
Existence of solutions for transversally elliptic left invariant differential operators on nilpotent Lie groups
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 of a nonlinear system modelling fluid flow in porous media.
Existence of solutions of a second order abstract functional Cauchy problem with nonlocal conditions
We establish the existence of mild, strong, classical solutions for a class of second order abstract functional differential equations with nonlocal conditions.