Nontrivial Topological Phases in Ternary Borides M_(2)XB_(2)(M=W,Mo;X=Co,Ni)

The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics.The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics.

NONTRIVIAL SOLUTION FOR A CLASS OF SEMILINEAR BIHARMONIC EQUATION INVOLVING CRITICAL EXPONENTS

In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.

THE EXISTENCE OF NONTRIVIAL SOLUTIONS TO A SEMILINEAR ELLIPTIC SYSTEM ON R N WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION

In this paper, we prove the existence of at least one positive solution pair （u, v）∈ H1（RN） × H1（RN） to the following semilinear elliptic system {-△u＋u=f（x,v）,x∈RN,-△u＋u=g（x,v）,x∈RN （0.1）,by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈C0（RN× R1） are that, f（x, t） and g（x, t） are superlinear at t = 0 as well as at t =＋∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245（2008）, 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem {-△u＋u=f（x,u）,x∈Ω,u∈H0^1（Ω） where Ω ∩→RN is bounded and a result of Li and Yang [G. Li and J. Yang： Communications in P.D.E. Vol. 29（2004） Nos.5＆ 6.pp.925-954, 2004] concerning （0.1） when f and g are asymptotically linear.

THE EXISTENCE OF NONTRIVIAL SOLUTIONS OF HAMILTONIAN SYSTEMS WITH LAGRANGIAN BOUNDARY CONDITIONS

Some theorems are obtained for the existence of nontrivial solutions of Hamiltonian systems with Lagrangian boundary conditions by the minimax methods.

A NONTRIVIAL SOLUTION OF A QUASILINEAR ELLIPTIC EQUATION VIA DUAL APPROACH

In this article, we are concerned with the existence of solutions of a quasilinear elliptic equation in R^N which includes the so-called modified nonlinear Schrodinger equation as a special case. Combining the dual approach and the nonsmooth critical point theory, we obtain the existence of a nontrivial solution.

STRUCTURE OF NONNEGATIVE NONTRIVIAL AND POSITIVE SOLUTIONS OF SINGULARLY PERTURBED p-LAPLACE EQUATIONS

Structure of nonnegative nontrivial and positive solutions was precisely studied for some singularly perturbed p-Laplace equations. By virtue of sub- and supersolution method, it is shown that there are many nonnegative nontrivial spike-layer solutions and positive intermediate spike-layer solutions. Moreover, the upper and lower bound on the measure of each spike-layer were estimated when the parameter is sufficiently small.

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

Five Nontrivial Solutions of p-Laplacian Problems Involving Critical Exponents and Singular Cylindrical Potential

In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem

MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS

In this paper, we are concerned with the following problem：{（-△）ku=λf（x）｜u｜q-2u＋g（x）｜u｜k＊-2u, x∈Ω, u∈H k0 （Ω）, where Ωis a bounded domain in RN with N ≥2k＋1, 1〈q〈2,λ〉0, f, g are continuous functions on Ω which are somewhere positive but which may change sign on Ω. k＊ = N2/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.

Quantum oscillations and nontrivial transport in (Bi0.92In0.08)2Se3

Quantum phase transition in topological insulators has drawn heightened attention in condensed matter physics and future device applications. Here we report the magnetotransport properties of single crystalline （Bi0.92In0.08）2Se3. The average mobility of^1000 cm2·V-1·s-1 is obtained from the Lorentz law at the low field （〈 3 T） up to 50 K. The quantum oscillations rise at a field of^5 T, revealing a high mobility of^1.4×104 cm2·V-1·s-1 at 2 K. The Dirac surface state is evident by the nontrivial Berry phase in the Landau-Fan diagram. The properties make the （Bi0.92In0.08）2Se3 a promising platform for the investigation of quantum phase transition in topological insulators.

Large Magnetoresistance and Nontrivial Berry Phase in Nb_(3)Sb Crystals with A15 Structure

Compounds with the A15 structure have attracted extensive attention due to their superconductivity and nontrivial topological band structures.We have successfully grown Nb_(3)Sb single crystals with the A15 structure and systematically measured the longitudinal resistivity,Hall resistivity and quantum oscillations in magnetization.Similar to other topological trivial/nontrivial semimetals,Nb_(3)Sb exhibits large magnetoresistance(MR)at low temperatures(717%,2 K and 9 T),unsaturating quadratic field dependence of MR and up-turn behavior in ρ_(xx)(T)curves under magnetic field,which is considered to result from a perfect hole-electron compensation,as evidenced by the Hall resistivity measurements.The nonzero Berry phase obtained from the de-Hass van Alphen(dHvA)oscillations demonstrates that Nb_(3)Sb is topologically nontrivial.These results indicate that Nb_(3)Sb superconductor is also a semimetal with large MR and nontrivial Berry phase.This indicates that Nb_(3)Sb may be another platform to search for the Majorana zero-energy mode.

Nontrivial Topological States in BaSn5 Superconductor Probed by de Haas–van Alphen Quantum Oscillations

We report the nontrivial topological states in an intrinsic type-Ⅱ superconductor BaSn_(5)(T_(c)∼4.4 K)probed by measuring the magnetization,specific heat,de Haas–van Alphen(dHvA)effect,and by performing first-principles calculations.The first-principles calculations reveal a topological nodal ring structure centered at the H point in the k_(z)=πplane of the Brillouin zone,which could be gapped by spin-orbit coupling(SOC),yielding relatively small gaps below and above the Fermi level of about 0.04 eV and 0.14 eV,respectively.The SOC also results in a pair of Dirac points along theΓ–A direction,located at∼0.2 eV above the Fermi level.The analysis of the dHvA quantum oscillations supports the calculations by revealing a nontrivial Berry phase originating from the hole and electron pockets related to the bands forming the Dirac cones.Thus,our study provides an excellent avenue for investigating the interplay between superconductivity and nontrivial topological states.

Existence of Nontrivial Solutions of A Nonlinear Volterra Integral Equation

Some new results on the existence of nonnegative nontrivial solutions of the nonlinear Volterra integral equation,u(x)= k(x,s)g(u(s))ds,(x≥0),are given and their applications are shown.

EXISTENCE OF NONTRIVIAL SOLUTION OF QUASILINEAR ELLIPTIC EIGENVALUE PROBLEM ON R^n WITH NATURAL GROWTH CONDITIONS

In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.

Rational design of superior catalysts from topological semimetals with nontrivial energy window

Materials featuring topological energy bands and nontrivial surface states hold significant promise in unlocking unprecedented opportunities for innovating electrocatalytic mechanism.However,it remains a challenge to realize superior topological catalysts which can carry both high catalytic activity and excellent catalytic stability.Here,we propose that a family of Ni-based binary materials hosting fantasying topological conjunct-nodalpoint state and a large nontrivial energy window(NEWD)represents an ideal choice for such superior topological catalysts in hydrogen evolution reaction.The presence of conjunct-nodal-points ensures long Fermi arcs on the surface,thereby enabling an extremely high catalytic activity.The NEWD plays a crucial role in stabilizing the high catalytic activity against external perturbations,such as strain and electron/hole injection.The roles for conjunctnodal-points and NEWD are substantiated by the observable weakening of catalytic performance during topological phase transitions,which result in the removal of the conjunct-nodal-points,NEWD and their corresponding long Fermi arcs.Our work unveils a hidden mechanism and opens a feasible route for developing superior quantum catalysts from novel topology point of view.

Nontrivial solutions for a class of fractional difference boundary value problems and fixed-point problems

In this work,we use the variant fountain theorem to study the existence of nontrivial solutions for the superquadratic fractional difference boundary value problem:{T△^(v)_(t-1)(t△^(v)_(v-1)x(t))=f(x(t+v-1)),t∈[0,T]N_(0),x(v-2)=[tΔ^(v)_(v-1)x(t)]_(t=T=0.The existence of nontrivial solutions is obtained in the case of super quadratic growth of the nonlinear term f by change of fountain theorem.

Nontrivial Solutions of Superquadratic Hamiltonian Systems with Lagrangian Boundary Conditionsand the L-index Theory

In this paper, the authors study the existence of nontrivial solutions for the Hamiltonian systems z（t） = J△↓H（t, z（t）） with Lagrangian boundary conditions, where ^H（t,z）=1/2（^B（t）z, z） ＋ ^H（t, z）,^B（t） is a semipositive symmetric continuous matrix and ^H（t, z） = satisfies a superquadratic condition at infinity. We also obtain a result about the L-index.

ON THE EXISTENCE OF NONTRIVIAL PERIODIC SOLUTIONS OF DIFFERENTIAL DIFFERENCE EQUATIONS

This paper cosiders the existence of nontrivial periodic solutions of the differentialdifference equationsx′(t)=-f(x(t-1)),x′(t)=-(f(x(t-1)+f(x(t-2))),and(x′(t)=f(x(t),y(t),x(t-1),y(t-1)),y′(t)=g(x(t),y(t),x(t-1),y(t-1)).)Some new existence criteria are obtained.

EXISTENCE OF NONTRIVIAL SOLUTIONS FOR CRITICAL SEMILINEAR BIHARMONIC EQUATIONS

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NONTRIVIAL SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR FOURTH-ORDER DIFFERENTIAL EQUATIONS

The singular boundary value problems for fourth-order differential equations are considered under some conditions concerning the first eigenvalues of the relevant linear operators. Sufficient conditions which guarantee the existence of nontrivial solutions are obtained. We use the topological degree to prove our main results.