Existence of solutions for elliptic systems with critical Sobolev exponent.
Extremal values of half-eigenvalues for -Laplacian with weights in balls.
Finite-energy sign-changing solutions with dihedral symmetry for the stationary nonlinear Schrödinger equation
We address the problem of the existence of finite energy solitary waves for nonlinear Klein-Gordon or Schrödinger type equations in , , where . Under natural conditions on the nonlinearity , we prove the existence of in any dimension . Our result complements earlier works of Bartsch and Willem and Lorca-Ubilla where solutions invariant under the action of are constructed. In contrast, the solutions we construct are invariant under the action of where denotes the dihedral group...
Focusing of spherical nonlinear pulses in R1+3. II. Nonlinear caustic.
We study spherical pulse like families of solutions to semilinear wave equattions in space time of dimension 1+3 as the pulses focus at a point and emerge outgoing. We emphasize the scales for which the incoming and outgoing waves behave linearly but the nonlinearity has a strong effect at the focus. The focus crossing is described by a scattering operator for the semilinear equation, which broadens the pulses. The relative errors in our approximate solutions are small in the L∞ norm.
Global and blowup solutions of quasilinear parabolic equation with critical Sobolev equation and lower energy initial value.
Global existence and blow up of solutions for a completely coupled Fujita type system of reaction-diffusion equations
We examine the parabolic system of three equations - Δu = , - Δv = , - Δw = , x ∈ , t > 0 with p, q, r positive numbers, N ≥ 1, and nonnegative, bounded continuous initial values. We obtain global existence and blow up unconditionally (that is, for any initial data). We prove that if pqr ≤ 1 then any solution is global; when pqr > 1 and max(α,β,γ) ≥ N/2 (α, β, γ are defined in terms of p, q, r) then every nontrivial solution exhibits a finite blow up time.
Global existence for nonlinear system of wave equations in 3-D domains
We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.
Hardy–Sobolev critical elliptic equations with boundary singularities
Heteroclinic orbits, mobility parameters and stability for thin film type equations.
Indefinite Quasilinear Neumann Problem on Unbounded Domains
We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.
Inégalités de Sobolev optimales et inégalités isopérimétriques sur les variétés
Inequalities for single crystal tube growth by edge-defined film-fed growth technique.
Lie symmetries and criticality of semilinear differential systems.
Life span of blow-up solutions for higher-order semilinear parabolic equations.
Life span of nonnegative solutions to certain quasilinear parabolic Cauchy problems.
Liouville results for -Laplace equations of Lane-Emden-Fowler type
Liouville-Gelfand type problems for the -laplacian on bounded domains of
Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators
We deal with maximum principles for a class of linear, degenerate elliptic differential operators of the second order. In particular the Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypothesis on the degeneracy set of the operator. We derive, as consequences of these principles, some generalized maximum principles and an a priori estimate on the solutions of the Dirichlet problem for the linear equation....
Mean curvature and least energy solutions for the critical Neumann problem with weight
In this paper we consider the Neumann problem involving a critical Sobolev exponent. We investigate a combined effect of the coefficient of the critical Sobolev nonlinearity and the mean curvature on the existence and nonexistence of solutions.
Monotonicity properties for ground states of the scalar field equation