Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations

[1]  Zongming Guo,et al.  Symmetry for elliptic equations in a half-space without strong maximum principle , 2004, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[2]  C. Gui,et al.  Estimates for boundary-bubbling solutions to an elliptic Neumann problem , 2002 .

[3]  N. Ghoussoub,et al.  ON A SINGULARLY PERTURBED NEUMANN PROBLEM WITH THE CRITICAL EXPONENT , 2001 .

[4]  Changshou Lin Locating the peaks of solutions via the maximum principle: I. The Neumann problem , 2001 .

[5]  Congming Li,et al.  Prescribing scalar curvature on Sn , 2001 .

[6]  Chiun-Chuan Chen,et al.  A spherical Harnack inequality for singular solutions of nonlinear elliptic equations , 2001 .

[7]  Chiun-Chuan Chen,et al.  Prescribing Scalar Curvature on $S^N$, Part 1: Apriori Estimates , 2001 .

[8]  Uniqueness Results through a Priori Estimates Part II. Dirichlet Problem , 2000 .

[9]  Changshou Lin Estimates of the scalar curvature equation via the method of moving planes III , 2000 .

[10]  B. Ou A uniqueness theorem for harmonic functions on the upper-half plane , 2000 .

[11]  Zheng-chao Han,et al.  The Yamabe problem on manifolds with boundary: Existence and compactness results , 1999 .

[12]  Meijun Zhu Uniqueness Results through a Priori Estimates I. A Three Dimensional Neumann Problem , 1999 .

[13]  Yanyan Li Harnack Type Inequality: the Method of Moving Planes , 1999 .

[14]  Chiun-Chuan Chen,et al.  On the asymptotic symmetry of singular solutions of the scalar curvature equations , 1999 .

[15]  Yuan Lou,et al.  Classifications of nonnegative solutions to some elliptic problems , 1999, Differential and Integral Equations.

[16]  Yanyan Li,et al.  YAMABE TYPE EQUATIONS ON THREE DIMENSIONAL RIEMANNIAN MANIFOLDS , 1999 .

[17]  Y. Li,et al.  Harnack Type Inequality : the Method of Moving Planes , 1999 .

[18]  Congming Li,et al.  INDEFINITE ELLIPTIC PROBLEMS WITH CRITICAL EXPONENTS , 1998 .

[19]  I. Shafrir,et al.  Existence of Positive Solutions of a Semilinear Elliptic Equation in Rn + with a Nonlinear Boundary Condition , 1998 .

[20]  Chiun-Chuan Chen,et al.  A sharp $\mathrm{sup} + \mathrm{inf}$ inequality for a nonlinear elliptic equation in $\mathbb{R}^2$ , 1998 .

[21]  Yanyan Li,et al.  Sharp Sobolev Inequalities Involving Boundary Terms , 1998 .

[22]  Chiun-Chuan Chen,et al.  Estimate of the conformal scalar curvature equation via the method of moving planes. II , 1998 .

[23]  Yanyan Li,et al.  Sharp Sobolev Inequalities Involving Boundary Terms , 1998 .

[24]  Henri Berestycki,et al.  Monotonicity for elliptic equations in unbounded Lipschitz domains , 1997 .

[25]  Chiun-Chuan Chen,et al.  Estimates of the conformal scalar curvature equation via the method of moving planes , 1997 .

[26]  Meijun Zhu,et al.  Sharp Sobolev trace inequalities on Riemannian manifolds with boundaries , 1997 .

[27]  Congming Li,et al.  A priori estimates for prescribing scalar curvature equations , 1997 .

[28]  Bianchi Gabriele,et al.  Non—existence of positive solutions to semilinear elliptic equations on r” or r” through the method of moving planes , 1997 .

[29]  L. Caffarelli,et al.  Inequalities for second-order elliptic equations with applications to unbounded domains I , 1996 .

[30]  Congming Li,et al.  Local asymptotic symmetry of singular solutions to nonlinear elliptic equations , 1996 .

[31]  Michel Chipot,et al.  On the solutions to some elliptic equations with nonlinear Neumann boundary conditions , 1996, Advances in Differential Equations.

[32]  R. Schoen,et al.  Prescribed scalar curvature on then-sphere , 1996 .

[33]  B. Ou Positive harmonic functions on the upper half space satisfying a nonlinear boundary condition , 1996 .

[34]  Yanyan Li The Nirenberg problem in a domain with boundary , 1995 .

[35]  Meijun Zhu,et al.  Uniqueness theorems through the method of moving spheres , 1995 .

[36]  M. Kiessling,et al.  Conformally invariant systems of nonlinear PDE of Liouville type , 1995 .

[37]  Yanyan Li Prescribing Scalar Curvature on Sn and Related Problems, Part I , 1995 .

[38]  Chiun-Chuan Chen,et al.  Local behavior of singular positive solutions of semilinear elliptic equations with Sobolev exponent , 1995 .

[39]  K. Chou,et al.  Asymptotic radial symmetry for solutions of Δu + eu = 0 in a punctured disc , 1994 .

[40]  Hong-Ming Yin,et al.  The profile near blowup time for solution of the heat equation with a nonlinear boundary condition , 1994 .

[41]  Bei Hu Nonexistence of a positive solution of the Laplace equation with a nonlinear boundary condition , 1994, Differential and Integral Equations.

[42]  S. Varadhan,et al.  The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains , 1994 .

[43]  Yanyan Li Prescribing scalar curvature on Sn and related problems , 1998 .

[44]  I. Shafrir,et al.  A sup + inf Inequality for Some Nonlinear Elliptic Equations Involving Exponential Nonlinearities , 1993 .

[45]  S. Chang,et al.  The scalar curvature equation on 2- and 3-spheres , 1993 .

[46]  Henri Berestycki,et al.  Travelling fronts in cylinders , 1992 .

[47]  Wenxiong Chen,et al.  Classification of solutions of some nonlinear elliptic equations , 1991 .

[48]  Henri Berestycki,et al.  On the method of moving planes and the sliding method , 1991 .

[49]  José F. Escobar Uniqueness theorems on conformal deformation of metrics, Sobolev inequalities, and an eigenvalue estimate , 1990 .

[50]  L. Nirenberg,et al.  Some Qualitative Properties of Solutions of Semilinear Elliptic Equations in Cylindrical Domains , 1990 .

[51]  Basilis Gidas,et al.  Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth , 1989 .

[52]  L. Nirenberg,et al.  Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations , 1988 .

[53]  H. Brezis Semilinear equations in ℝN without condition at infinity , 1984 .

[54]  H. Brezis Semilinear Equations in RN without conditions at infinity , 1983 .

[55]  Basilis Gidas,et al.  Global and local behavior of positive solutions of nonlinear elliptic equations , 1981 .

[56]  B. Gidas,et al.  Symmetry of positive solutions of nonlinear elliptic equations in R , 1981 .

[57]  B. Gidas,et al.  Symmetry and related properties via the maximum principle , 1979 .

[58]  M. Obata The conjectures on conformal transformations of Riemannian manifolds , 1971 .

[59]  James Serrin,et al.  A symmetry problem in potential theory , 1971 .