On a singular class of elliptic systems involving critical growth in \(\mathbb R^2\)

DOI10.1016/j.nonrwa.2010.09.001zbMath1206.35095OpenAlexW1969455286MaRDI QIDQ619734

Manassés de Souza

Publication date: 18 January 2011

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2010.09.001

zbMATH Keywords

variational methodscritical exponentscritical pointselliptic systemsTrudinger-Moser inequality

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for elliptic systems (35J50) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Second-order elliptic systems (35J47) Singular elliptic equations (35J75)

Related Items (14)

On a nonhomogeneous Kirchhoff type elliptic system with the singular Trudinger-Moser growth ⋮ Kirchhoff type elliptic systems with exponential growth nonlinearities ⋮ Existence and multiplicity of symmetric solutions for a class of singular elliptic problems ⋮ Ground state solutions for a Kirchhoff‐type elliptic system involving critical exponential growth nonlinearities ⋮ Biharmonic Kirchhoff type elliptic systems with the singular exponential nonlinearities in \(\mathbb{R}^4\) ⋮ Existence and multiplicity of symmetric solutions for semilinear elliptic equations with singular potentials and critical Hardy-Sobolev exponents ⋮ Multiple symmetric results for quasilinear elliptic systems involving singular potentials and critical Sobolev exponents in \(\mathbb{R}^N\) ⋮ On a singular class of Hamiltonian systems in dimension two ⋮ Positive symmetric solutions for a class of critical quasilinear elliptic problems in \(\mathbb R^N\) ⋮ Existence of solutions for Kirchhoff type systems involving \(Q\)-Laplacian operator in Heisenberg group ⋮ Standing wave solutions for a class of nonhomogeneous systems in dimension two ⋮ Multiple solutions for \(N\)-Kirchhoff type problems with critical exponential growth in \(\mathbb{R}^N\) ⋮ On a class of nonhomogeneous elliptic equation on compact Riemannian manifold without boundary ⋮ Existence and multiplicity of solutions to a Kirchhoff type elliptic system with Trudinger-Moser growth

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear scalar field equations. I: Existence of a ground state
• The concentration-compactness principle in the calculus of variations. The limit case. I
• A nonhomogeneous elliptic problem involving critical growth in dimension two
• Elliptic systems involving critical growth in dimension two
• Lectures on the Ekeland variational principle with applications and detours. Lectures delivered at the Indian Institute of Science, Bangalore, India under the T.I.F.R.-I.I.Sc. programme in applications of mathematics
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• Variational methods for potential operator equations: with applications to nonlinear elliptic equations
• Semilinear Dirichlet problems for the \(N\)-Laplacian in \(\mathbb{R}^ N\) with nonlinearities in the critical growth range
• A singular Moser-Trudinger embedding and its applications
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Phenomena of critical exponent in ℝ²
• On an inequality by N. Trudinger and J. Moser and related elliptic equations

This page was built for publication: On a singular class of elliptic systems involving critical growth in \(\mathbb R^2\)