On inequalities between solutions of first order partial differential-functional equations
On inertial manifolds for reaction-diffusion equations on genuinely high-dimensional thin domains
We study a family of semilinear reaction-diffusion equations on spatial domains , ε > 0, in lying close to a k-dimensional submanifold ℳ of . As ε → 0⁺, the domains collapse onto (a subset of) ℳ. As proved in [15], the above family has a limit equation, which is an abstract semilinear parabolic equation defined on a certain limit phase space denoted by . The definition of , given in the above paper, is very abstract. One of the objectives of this paper is to give more manageable characterizations...
On infinitely many solutions of a semilinear elliptic eigenvalue problem
On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator.
On Kelvin type transformation for Weinstein operator
The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator on is proved. In this note there is shown that in the cases , no other transforms of this kind exist and for case , all such transforms are described.
On Kirchhoff type problems involving critical and singular nonlinearities
In this paper, we are interested in multiple positive solutions for the Kirchhoff type problem ⎧ in Ω ⎨ ⎩ u = 0 on ∂Ω, where Ω ⊂ ℝ³ is a smooth bounded domain, 0∈Ω, 1 < q < 2, λ is a positive parameter and β satisfies some inequalities. We obtain the existence of a positive ground state solution and multiple positive solutions via the Nehari manifold method.
On Korn's second inequality
On KP-II type equations on cylinders
On -regularity for the gradient of a weak solution to nonlinear elliptic systems
Interior -regularity for the gradient of a weak solution to nonlinear second order elliptic systems is investigated.
On -estimates for hyperbolic systems
On -estimates for the time dependent Schrödinger operator on .
On L2 Decay of Weak Solutions of the Navier-Stokes Equations in Rn.
On large amplitude solutions of the Yang-Mills equations in Minkowski space-time
On L...-decay and scattering for nonlinear Klein-Gordon equations.
On Liouville theorem and apriori estimates for the scalar curvature equations
On Liouville theorem and Hölder continuity of weak solutions to some quasilinear elliptic systems of higher order
The aim of this paper is to show that the Liouville-type property is a sufficient and necessary condition for the regularity of weak solutions of quasilinear elliptic systems of higher orders.
On Lipschitz continuity of the solution map for two-dimensional wave maps
On Lyapunov-type inequalities for two-dimensional nonlinear partial systems.
On Maximal Functions and Parabolic Limits.
On maximum principle for weak subsolutions of degenerate parabolic linear equations
Sufficient conditions are obtained so that a weak subsolution of , bounded from above on the parabolic boundary of the cylinder , turns out to be bounded from above in .