Existence of global solutions for a predator-prey model with cross-diffusion.
Existence of global solutions for a system of reaction-diffusion equations with exponential nonlinearity.
Existence of global solutions for a system of reaction-diffusion equations having a triangular matrix.
Existence of global solutions for systems of reaction-diffusion equations on unbounded domains.
Existence of global solutions of the Yang-Mills, Higgs and spinor field equations in dimensions
Existence of global solutions to a quasilinear wave equation with general nonlinear damping.
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional.
Existence of global solutions to reaction-diffusion systems with nonhomogeneous boundary conditions via a Lyapunov functional.
Existence of Global Solutions to Supercritical Semilinear Wave Equations
∗The author was partially supported by Alexander von Humboldt Foundation and the Contract MM-516 with the Bulgarian Ministry of Education, Science and Thechnology.In this work we study the existence of global solution to the semilinear wave equation (1.1) (∂2t − ∆)u = F(u), where F(u) = O(|u|^λ) near |u| = 0 and λ > 1. Here and below ∆ denotes the Laplace operator on R^n. The existence of solutions with small initial data, for the case of space dimensions n = 3 was studied by F. John in [13],...
Existence of global solutions to the 2-D subcritical dissipative quasi-geostrophic equation and persistency of the initial regularity.
Existence of global solutions to the Cauchy problem for the seminlinear dissipative wave equations.
Existence of global weak solutions to a symmetrically hyperbolic system with a source.
Existence of infinitely many distinct solutions to the quasirelativistic Hartree-Fock equations.
Existence of infinitely many nodal solutions for a superlinear Neumann boundary value problem.
Existence of infinitely many solutions for degenerate and singular elliptic systems with indefinite concave nonlinearities.
Existence of infinitely many solutions for elliptic boundary-value problems with nonsymmetrical critical nonlinearity.
Existence of infinitely many weak solutions for some quasilinear $\vec {p}(x)$-elliptic Neumann problems
We consider the following quasilinear Neumann boundary-value problem of the type $$ \begin {cases} -\displaystyle \sum _{i=1}^{N}\frac {\partial }{\partial x_{i}}a_{i}\Big (x,\frac {\partial u}{\partial x_{i}}\Big ) + b(x)|u|^{p_{0}(x)-2}u = f(x,u)+ g(x,u) &\text {in} \ \Omega , \\ \quad \dfrac {\partial u}{\partial \gamma } = 0 &\text {on} \ \partial \Omega . \end {cases} $$ We prove the existence of infinitely many weak solutions for our equation in the anisotropic variable exponent Sobolev...
Existence of entropy solutions for a reacting Euler system.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities.
Existence of Local Smooth Solution for a Generalized Zakharov System.