𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Existence and Bifurcation of the Positive Solutions for a Semilinear Equation with Critical Exponent

✍ Scribed by Yinbin Deng; Yi Li

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
899 KB
Volume
130
Category
Article
ISSN
0022-0396

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we consider the semilinear elliptic equation
For p=2NΓ‚(N&2), we show that there exists a positive constant +\>0 such that (V) + possesses at least one solution if + # (0, +\) and no solutions if +>+\. Furthermore, (V) + possesses a unique solution when +=+\, and at least two solutions when + # (0, +\*) and 22 are some given constants and f (x) is some given function in H &1 (R N ) such that f (x) 0, f (x) 0 in R N .

πŸ“œ SIMILAR VOLUMES

Critical Exponents for the Blowup of Sol
Critical Exponents for the Blowup of Solutions with Sign Changes in a Semilinear Parabolic Equation, II
✍ Noriko Mizoguchi; Eiji Yanagida πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 353 KB

The blowup of solutions of the Cauchy problem { u t =u xx + |u| p&1 u u(x, 0)=u 0 (x) in R\\_(0, ), in R is studied. Let 4 k be the set of functions on R which change sign k times. It is shown that for p k =1+2Γ‚(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T

On the Existence of Positive Solutions f
On the Existence of Positive Solutions for Semilinear Elliptic Equations in the Annulus
✍ H.Y. Wang πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 180 KB

We study the existence of positive radial solutions of \(A u+g(|x|) f(u)=0\) in annuli with Dirichlet (Dirichlet/Neumann) boundary conditions. We prove that the problems have positive radial solutions on any annulus if \(f\) is sublinear at 0 and \(\infty . \quad C 1994\) Academic Press, Inc.

Existence and Multiplicity of Solutions
Existence and Multiplicity of Solutions for a Class of Semilinear Elliptic Equations
✍ Shui-Qiang Liu; Chun-Lei Tang πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 92 KB

The existence and multiplicity results are obtained for solutions of a class of the Dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods, respectively.