𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Solvability of perturbed elliptic equations with critical growth exponent for the gradient

✍ Scribed by Rüdiger Landes

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
582 KB
Volume
139
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Existence and Multiplicity of Nodal Solu
Existence and Multiplicity of Nodal Solutions for Nonlinear Elliptic Equations with Critical Sobolev Growth
✍ E. Hebey; M. Vaugon 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 594 KB

Let \(\Omega\) be a smooth bounded domain of \(\mathbb{R}^{n}, n \geqslant 3\), and let \(a(x)\) and \(f(x)\) be two smooth functions defined on a neighbourhood of \(\Omega\). First we study the existence of nodal solutions for the equation \(\Delta u+a(x) u=f(x)|u|^{4 /(n-2)} u\) on \(\Omega, u=0\)

Existence and Bifurcation of the Positiv
Existence and Bifurcation of the Positive Solutions for a Semilinear Equation with Critical Exponent
✍ Yinbin Deng; Yi Li 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 899 KB

In this paper, we consider the semilinear elliptic equation For p=2NÂ(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 s

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 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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+2Â(k+1), k=0, 1, 2, ... , any solution with u 0 # 4 k blows up in finite time if 1 p k . T