Existence and perturbation of principal eigenvalues for a periodic-parabolic problem.
Existence and regularity for semilinear parabolic evolution equations
Existence and regularity of a global attractor for doubly nonlinear parabolic equations.
Existence and regularity of optimal solution for a dead oil isotherm problem.
Existence and Regularity of Solutions for a Semilinear First-Order Equation on the Torus.
Existence and stability of periodic solutions for a nonlocal evolution population problem.
The theory of maximal monotone operators is applied to prove the existence of weak periodic solutions for a nonlinear nonlocal problem. The stability of these solutions is a consequence of the Lipschitz continuous assumption on the diffusivity matrix and the death rate.
Existence and stability results of nonlinear higher-order wave equation with a nonlinear source term and a delay term
We consider the initial-boundary value problem for a nonlinear higher-order nonlinear hyperbolic equation in a bounded domain. The existence of global weak solutions for this problem is established by using the potential well theory combined with Faedo-Galarkin method. We also established the asymptotic behavior of global solutions as by applying the Lyapunov method.
Existence and stability theorems for abstract parabolic equations, and some of their applications
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary.
Existence and uniqueness for a nonlinear dispersive equation.
Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Existence and uniqueness of periodic solutions for a model of contaminant flow in porous medium.
Existence and uniqueness of periodic solutions for a nonlinear reaction-diffusion problem.
We consider a class of degenerate reaction-diffusion equations on a bounded domain with nonlinear flux on the boundary. These problems arise in the mathematical modelling of flow through porous media. We prove, under appropriate hypothesis, the existence and uniqueness of the nonnegative weak periodic solution. To establish our result, we use the Schauder fixed point theorem and some regularizing arguments.
Existence and uniqueness of solutions for a semilinear elliptic system.
Existence and Uniqueness of Solutions for the Generalized Korteweg de Vries Equations.
Existence and Uniqueness of Solutions of Nonlinear Neumann Problems.
Existence and uniqueness of solutions to wave equations with nonlinear degenerate damping and source terms