Critical exponent problem in \(\mathbb{R}^ 2\)-border-line between existence and non-existence of positive solutions for Dirichlet problem.

Publication date: 4 February 2002

Published in: Advances in Differential Equations (Search for Journal in Brave)

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear boundary value problems for ordinary differential equations (34B15) Critical exponents in context of PDEs (35B33)

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Uniqueness of positive solutions of a \(n\)-Laplace equation in a ball in \(\mathbb{R}^n\) with exponential nonlinearity ⋮ A global multiplicity result for \(N\)-Laplacian with critical nonlinearity of concave-convex type ⋮ Failure of Palais-Smale condition and blow-up analysis for the critical exponent problem in \(\mathbb{R}^2\) ⋮ Bubbling nodal solutions for a large perturbation of the Moser-Trudinger equation on planar domains ⋮ Isolated singularities for the exponential type semilinear elliptic equation in ℝ² ⋮ Multiplicity results for semilinear heterogeneous problems in exterior domains of \(\mathbb{R}^2\) involving subcritical or critical nonlinearities à la Trudinger-Moser ⋮ Sharp threshold nonlinearity for maximizing the Trudinger-Moser inequalities ⋮ On heterogeneous radially symmetric semilinear elliptic equations with critical nonlinearities in \(\mathbb{R}^2\)

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