ANALYSIS OF STRONG SINGULARITIES FOR NONLINEAR HYPERBOLIC EQUATIONS

In this paper we review our some results about the strongly singular (discontinuous,measure, or delta function) problems for nonlinear hyperbolic equations.     

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR NONLINEAR PARABOLIC EQUATIONS WITH VARIABLE EXPONENT OF NONLINEARITY＊

The authors of this article study the existence and uniqueness of weak solutions of the initial-boundary value problem for ut =div((|u|σ + do)|▽u|P(x,t)-2▽u) +f(x,t) (0 ＜ σ ＜ 2).They apply the method o...     

THE NUMBER OF NONTRIVIAL SOLUTIONS TO HAMMERSTEIN NONLINEAR INTEGRAL EQUATIONS

In this paper,the author improves some results of Rabinowitz about the existence ofinfinitely many nontrivial solutions to Hammerstein nonlinear integral equations andgives some applications to the two-point boundary value problems for nonlinear ordinarydifferential equations.     

NONTRIVIAL SOLUTIONS OF THE DIRICHLET PROBLEM FOR A CLASS OF NONLINEAR ELLIPTIC EQUATIONS

Under the mild conditions by using the theory of the generalized Sobolev space and minimax theory we get the existence of solutions for a wide class of nonlinear Dirichlet problem as follows where Q is a bounded domain in . This equation is the Euler equation of the functional where     

THE GLOBAL SOLUTION AND“BLOW UPPHENOMENON FOR A CLASS OF SYSTEM OF NONLINEAR SCHR(?)DINGER EQUATIONS WITH THE MAGNETIC FIELD EFFECT

In this paper,the auther considers following initial value problem for the system ofnonlinear Schrdinger equation with the magnetic field effectiε_t-△ε+βq(丨ε丨~2)ε+ηε×(ε×ε)=0 (1.1)ε丨t_0=ε_0(x),x∈R~2,(1.2)where β,η are real constants,ε=(ε~1,ε~2,ε~3).First,the existence of the global solutionfor problem(1.1),(1.2)is established by means of the method of integral estimates,andthen the “blow up” theorem is obtained nuder some conditions.     

ON THE BOUNDARY ESTIMATION OF THE SOLUTION OF STRONG QUASI-LINEAR ELLIPTIC EQUATIONS

In [1] we investigated the problems of calculus of variations with strong non-linearity. In[2] we already indecated its Euler equation is evidently the following elliptic type equation of divergent form with strongly increasing coefficient     

THE MAPPING RELATION AMONG SOLUTION OF SOME NONLINEAR EQUATIONS

Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.     

STABILITY OF THE MILD SOLUTION OF STOCHASTIC NONLINEAR EVOLUTION DIFFERENTIAL EQUATIONS

In this paper, we consider the stability problem associated with the mild solutions of stochastic nonlinear evolution differential equations in Hilbert space under hypothesis which is weaker than Lipschitz condition. And the result is established by employing the Ito-type inequality and the extension of the Bihari's inequality.     

PERIODIC SOLUTIONS OF SCALAR NEUTRAL VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper deals with the existence and uniqueness of periodic solutions of the following scalar neutral Volterra integro-differential equation with infinite delaywhere a, C, D, f are continuous functions, also a(t + T) = a(t), C(t + T,s + T) = C(t, s), D(t + T,s + T) = D(t, s), f(t + T) = f(t). Sufficient conditions on the existence and uniqueness of periodic solution to this equation are obtained by the contraction mapping theorem.     

THE EXISTENCE OF ALMOST PERIODIC SOLUTION TO NONLINEAR DIFFERENTIAL EQUATIONS

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