A. We consider the semi-linear elliptic PDEs driven by the fractional Laplacian: { (−∆)su = f (x, u), in Ω, u = 0, in Rn\Ω. By the Mountain Pass Theorem and some other nonlinear analysis methods, the existence and multiplicity of non-trivial solutions for the above equation are established. The validity of the Palais-Smale condition without AmbrosettiRabinowitz condition for non-local el...

We construct local minimum solutions for the semilinear bistable equation by minimizing the corresponding functional near some approximate solutions, under the hypothesis that certain global minimum solutions are isolated. The key is a certain characterization of Palais-Smale sequences and a proof that the functional takes higher values away from the approximate solutions.

In this paper, we study the bubbling phenomena of weak solution sequences of a class of degenerate quasilinear elliptic systems of m-harmonic type. We prove that, under appropriate conditions, the energy is preserved during the bubbling process. The results apply to m-harmonic maps from a manifold Ω to a homogeneous space, and to m-harmonic maps with constant volumes, and also to certain Palais...

It is shown that the nonhomogeneous Dirichlet and Neuman problems for the 2nd-order Seiberg-Witten equation on a compact 4-manifold X admit a regular solution once the nonhomogeneous Palais-Smale condition is satisfied. The approach consists in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation. The gauge invariance of the functional allows to restrict th...

We consider a class of variational systems in R N of the form where a; b : R N ! R are continuous functions which are coercive; i.e., a(x) and b(x) approach plus innnity as x approaches plus innnity. Under appropriate growth and regularity conditions on the nonlinearities Fu(:) and Fv (:), the (weak) solutions are precisely the critical points of a related functional deened on a Hilbert space o...

Proof. In [4] it was shown that ps<pt for any two positive integers 5 and / for which s<t. Hence the lemma is true if 7 and 5 are each integers. Since, for 5 finite, ps<p(s + l) ^uo)^p(oo*+oj) and ps<p(s + l) ^pco*^p(co*+o}), it follows that the lemma is true if one of the elements 7 or 5 is finite, and the other is not. Suppose that pu and pu* are demonstrated to be incomparable order types.2 ...

In this study, nanoscale zero-valent copper (nZVC) as catalyst activated persulfate (PS) was used for the degradation of p-chlorophenol (p-CP) under ultrasonic (US) irradiation in aqueous solution. The effect of different operational parameters such as solution pH (3.5-10.5), PS concentration (1-7.5 mm/L), nZVC dosage (5-35 mg/L) and initial p-CP concentration (10-100 mg/L) were evaluated at di...

Highly monodisperse polystyrene/poly(N-isopropylmethacrylamide) (PS-PNIPMAM) core-shell composite microgels were synthesized and further nanoengineered in either ellipsoidal, faceted or bowl-shaped particles. Beside their anisotropy in shape, the microgel design enables an exquisite control of the particle conformation, size and interactions from swollen and hydrophilic to collapsed and hydroph...

Abstract A 33.6 ps LSB Time-to-Digital converter was designed in 130 nm BiCMOS technology. The core of the is a differential 9-stage ring oscillator, based on multi-path architecture. novel version this design proposed, along with an analytical model linearity. allowed us to understand source performance superiority (in terms linearity) our and predict further improvements. oscillator integrate...

In this paper, we introduce the notion of fuzzy dot PS-subalgebras in PSalgebras and establish its various properties.