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Phenomena of critical exponent in \(\mathbb{R}{} ^ 2\). (English) Zbl 0768.35024

(Authors’ summary.) We make an attempt to explain the critical phenomena in \(\mathbb{R}^ 2\). We do this by exhibiting a class of functions having \(e^{u^ 2}\) growth and for which \[ -\Delta u=f(u) \quad\text{in } B(R), \qquad u>0, \qquad u=0 \quad \text{ on } \partial B(R) \] do not admit a solution when \(R\) is sufficiently small, where \(B(R)\) denotes the ball of radius \(R\) in \(\mathbb{R}^ 2\).
Reviewer: S.Tersian (Russe)

MSC:

35J60 Nonlinear elliptic equations
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