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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\},$$1\le p<\infty, in the infinitely fast/infinitely slow diffusion limit p\to\infty...  作者：Luiz Fichmann 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.138 (1), pp.1-18ZBMATH 摘要：A discrete-time version of the parabolic scalar equation is investigated. Consider a sequence \{u_n\}_{n\in\bbfN} of functions u_n\in H^1_0=\{p:[0,1]\to\bbfR: p is absolutely continuous with p(0)=p(1)=0 and p'\in L_2(0,1)\} satisfying:$$u_{n+1}-u_n=\varepsilon\Delta u_{n...
 作者：Hiroshi Isozaki 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.138 (1), pp.19-54ZBMATH 摘要：It is proved that the scattering matrix at a fixed positive energy determines uniquely the wave velocity which is assumed to depend asymptotically on one variable (the vertical coordinate). The velocity approaches its limit at infinity at an exponential rate. This limit is a piec...
 作者：Micha{\l} Kowalczyk 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.138 (1), pp.55-85ZBMATH 摘要：The author studies the following single reaction-diffusion equation (Allen-Cahn equation) in a bounded domain $$u_t= \Delta u- \varepsilon^{-2} F'(u)\text { in }\Omega \times (0,\infty)$$ with the Neumann boundary condition. $F$ is a double-well type function. Because of the smal...
 作者：E.N. Dancer , D. Daners 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.138 (1), pp.86-132ZBMATH 摘要：The aim of this very important paper is to study how the solutions of the linear or nonlinear equation $$-\Delta u=f(u) \quad\text{in }\Omega_n, \qquad \frac{\partial u}{\partial\nu}+ \beta_0 u=0 \quad\text{on }\partial\Omega_n$$ behave as the domains $\Omega_n$ approach an open ...
 作者：Patrick Habets , Enrico Serra , Massimo Tarallo 来源：[J].J. Differ. Equations(IF 1.48), 1997, Vol.138 (1), pp.133-156ZBMATH 摘要：Let $\Omega$ be a bounded domain in $\bbfR^N$ and $\lambda_n$ the $n$th eigenvalue of $-\Delta$ with homogeneous Dirichlet condition. The authors consider the elliptic problem at resonance \Delta u+\lambda_nu+ g(x,u)= 0\quad\text{in }\Omega,\quad u= 0\quad\text{on }\partial\Ome...