66 research outputs found
The photo-catalytic activities of MP (M = Ba, Ca, Cu, Sr, Ag; P = PO43-, HPO42-) microparticles
No full textFor the good performance of apatite-based materials in the removal of dyes and their environment-friendly advantage, five kinds of apatite microparticles of MP (M = Ba, Ca, Cu, Sr, Ag; P = PO43-, HPO42-) were synthesized by a simple precipitation method and their photo-catalytic properties were invested. Better performance in the decolorization of methyl orange (MO) under the assistance of H2O2 than that of TiO2 were obtained for all the MPs. The photo-catalytic activity was mainly affected by surface area, energy band, impurity, crystallinity and crystal structure. The DFT calculation results demonstrated that the 2p of O and 3p of Pin PO43- played the main role in the photo-catalytic process. This work would be helpful to design and synthesize low cost apatite materials with good photo-catalytic performance. (C) 2013 Elsevier B.V. All rights reserved
On positive solutions of quasilinear elliptic systems
Get PDFsummary:In this paper, we consider the existence and nonexistence of positive solutions of degenerate elliptic systems where is the -Laplace operator, and is a -domain in . We prove an analogue of [7, 16] for the eigenvalue problem with , and obtain a non-existence result of positive solutions for the general systems
A generalized Fucik type eigenvalue problem for p-Laplacian
Get PDFIn this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional Laplace type differential equations
where We obtain a explicit characterization of Fucik spectrum i.e., for which the (*) has a nontrivial solution
Some surprising results on one-dimensional elliptic boundary value blow-up problem
No full textIn this paper we consider the one-dimensional elliptic boundary blow-up problem ∆p(u) = f(u), a < x < b, u(a) = u(b) = + ∞. We show that the structure of the solutions can be very rich even for a simple function f, which indicates that a similar results might hold also in higher dimensional spaces
Multiple solutions for prescribed boundary value problem
No full textWe, in this paper, consider the semilinear elliptic boundary value problem
- ∆u = f(x, u) in Ω and u = g on ∂Ω
and the corresponding Bolza problem
x'' + ∂V(t, x) =0, x(0)= x0, x(T)= x1, where Ω is a bounded open subset in R^n with C² boundary and g is a given continuous function on the boundary of Ω; and T is the given traveling time, x0,x1 are two fixed points in the state space Rn. Under certain conditions on f and V, we show that the above problems have infinitely many solution
Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent
No full textIn this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent where , is a bounded -domain , is a bifurcation parameter. Brezis and Nirenberg [2] showed that a lower order (non-negative) perturbation can contribute to regain the compactness and whence yields existence of solutions. We study the equation with an indefinite perturbation and prove a bifurcation result of two solutions for this equation
Hölder Continuity of the Inverse ofp-Laplacian
No full textAbstractIn this note, we study the inverse operator (−Δp)−1ofp-Lapalcian on a bounded domain Ω⊂Rn. We show that (−Δp)−1:W−1,p′(Ω)→W1,p0(Ω) is Hölder continuous and is a compact operator fromV(q,s)toW1,p0(Ω),s∈(0,p′),q>p∗ the conjugate of critical Sobolev exponent. As an application, we study existence of positive solutions of two nonlinear elliptic equations
Boundary blow-up insemilinear elliptic problems with singular weights at the boundary [Elektronisk resurs]
No full textIn this paper, we study under what conditions on m(x) and f(u) the problem Δu=m(x)f(u) has a solution in a bounded domain D, which tends to infinity, as x tends to the boundary. We show that if m(x) is singular at the boundary of D, except that the Keller-Osserman condition must hold, the growth of f at the infinity has to be slow for a solution to exist. Some existence results have been established.</p
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