A nonlinear second order problem with a nonlocal boundary condition.
A nonlinear transmission problem with time dependent coefficients.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value.
A nonlocal elliptic equation in a bounded domain
The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form , in a bounded domain Ω in ℝⁿ with some growth assumptions on the nonlinear terms f and g is proved. The method based on the Krasnosel’skiĭ Fixed Point Theorem enables us to find many solutions as well.
A nonlocal mixed semilinear problem for second-order hyperbolic equations.
A note about a priori estimates for indefinite problems in unbounded domains.
A note on asymptotic expansion for a periodic boundary condition
The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in D.
A note on bounds for non-linear multivalued homogenized operators
In this paper we study the behaviour of maximal monotone multivalued highly oscillatory operators. We construct Reuss-Voigt-Wiener and Hashin-Shtrikmann type bounds for the minimal sections of G-limits of multivalued operators by using variational convergence and convex analysis.
A Note on Div-Curl Lemma
2000 Mathematics Subject Classification: 42B30, 46E35, 35B65.We prove two results concerning the div-curl lemma without assuming any sort of exact cancellation, namely the divergence and curl need not be zero, and which include as a particular case, the result of [3].
A note on local smoothing effects for the unitary group associated with the KdV equation.
A note on maximal estimates for stochastic convolutions
In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.
A Note on Maximal Rate of Decay for Solutions to Some Linear Wave Equations.
A note on measure-valued solutions to the full Euler system
We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.
A note on nodal non-radially symmetric solutions to Emden-Fowler equations.
A note on nonlinear elliptic systems involving measures.
A note on nontrivial periodic solutions of dynamical systems with subquadratic potential.
We obtain non-constant periodic solutions for a class of second-order autonomous dynamic systems whose potential is subquadratic at infinity. We give a theorem on conjugate points for convex potentials.
A note on regular points for solutions of nonlinear elliptic systems
It is shown in this paper that gradient of vector valued function solution of a nonlinear elliptic system, cannot be too close to a straight line without being regular.
A note on resonant frequencies for a system of elastic wave equations.
A note on stability for linear partial differential equations
A note on the bifurcation of solutions for an elliptic sublinear problem