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 作者：Paolo Marcellini , Keith Miller 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.137 (1), pp.1-53ZBMATH 摘要：It is well-known that the Dirichlet problem for the equation of prescribed mean curvature $$\text{div}((1+|Du|^2)^{-1/2}Du)+ h(x)= 0\quad\text{in }\Omega\subset\bbfR^n,\ u=\Phi\quad\text{on }\partial\Omega\tag1$$ has no classical solution if the curvature function $h$ is too big....
 作者：Avner Friedman , Bei Hu , Yong Liu 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.137 (1), pp.54-93ZBMATH 摘要：Let $\varepsilon\in (0,1]$ and let $\Omega_\varepsilon \subset\bbfR^2$ be the domain bounded by the lines $\{x=\pm a\}$, $\{y=b\}$ and $$\Gamma_\varepsilon:\ y_\varepsilon (x)=f_0(x)+ \varepsilon f_1(x,x/ \varepsilon)+ \varepsilon^2f_2(x,x/ \varepsilon,x/ \varepsilon^2)...  作者：Henryk \D{Z}o{\l}\c{a}dek 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.137 (1), pp.94-118ZBMATH 摘要：As is well-known, the general integral of the last center case for a real quadratic field (which can generate three limit cycles after small perturbations) can be obtained by applying to the field a complex linear transformation x={1\over 2i} (u-v), y={1\over 2} (u+v) and tra...  作者：Avner Friedman , Bei Hu 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.137 (1), pp.119-165ZBMATH 摘要：The paper is concerned with a free boundary value problem for the Laplace and heat equations. A part of the boundary varies in time and is rapidly oscillating in space at each time. The existence and uniqueness of the solution as well as its time asymptotics are established. Prec...  作者：L.C. Evans , M. Feldman , R.F. Gariepy 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.137 (1), pp.166-209ZBMATH 摘要：The authors study the behaviour of solutions u_p of the initial value problem$$u_{p,t}- \Delta_pu_p= 0\quad\text{in }\bbfR^n\times (0,\infty),\quad u_p=g\quad\text{in }\bbfR^n\times\{t= 0\},$$1\le p<\infty, in the infinitely fast/infinitely slow diffusion limit p\to\infty...  作者：Xiaoxin Chen 来源：[J].Ann. Differ. Equations, 1997, Vol.13 (2), pp.107-118ZBMATH 摘要：The characteristic exponents of the periodic system x''+p(t) x'+q(t) x=0 are investigated. In the case when q(t) \neq 0 and \int_{0}^{T} p(t) dt \neq 0 some results are obtained. These results generalize the results of the autonomous system x''+p x'+q x=0.  作者：Zhaosheng Feng , Shuming Fei 来源：[J].Ann. Differ. Equations, 1997, Vol.13 (2), pp.119-124ZBMATH 摘要：Summary: We investigate the Schr\"odinger equation$$iu_t+ u_{xx}- u_{yy}+\beta|u|^2u= 0$$and the Klein-Gordon equation$$u_{tt}- (u_{xx}+ u_{yy})+ \alpha^2u+ \beta|u|^2u= 0$$and obtain a class of analytic solutions.  作者：Lin Guo , Guowei Chen 来源：[J].Ann. Differ. Equations, 1997, Vol.13 (2), pp.125-139ZBMATH 摘要：The authors consider a cubic Van der Pol equation as follows$$\ddot x-(b_{01} +b_{21} x^2+b_{02} \dot x+b_{12} x\dot x) \dot x+(1-b_{20} x-b_{30} x^2)x=0$$with b^2_{20} +4b_{30} <0. Sufficient conditions for the existence and non-existence of limit cycles are given in terms o...  作者：Weizhang Huang 来源：[J].Ann. Differ. Equations, 1997, Vol.13 (2), pp.140-145ZBMATH 摘要：This note concerns the problem$$\varepsilon^2y''-f(x,y,y')=g(x,Ty),\qquad y(0)=A,\quad ay(1)+by'(1)=B,\tag 1 where $y\in\bbfR^n$, $Ty=\int_0^xK(t)y(t) dt$, $K(x)= \text{diag} (K_1(x),\cdots,K_n(x))$ and $\varepsilon>0$. Assumptions are given to prove the existence of a solutio...
 作者：Wei Jiang 来源：[J].Ann. Differ. Equations, 1997, Vol.13 (2), pp.146-153ZBMATH 摘要：It is considered a deterministic optimal consumption-investment (or production-investment) model with two assets paying different interest. The portfolio evolution is described by linear equations with delay. The aim is to maximize the total terminal wealth. To find a solution, t...