Existence of a nontrivial solution for a \((p,q)\)-Laplacian equation with \(p\)-critical exponent in \(\mathbb{R}^{N}\)

DOI10.1186/s13661-014-0236-xzbMath1311.35127OpenAlexW2144075656WikidataQ59320013 ScholiaQ59320013MaRDI QIDQ2263518

Grey Ercole, Marcio Fialho Chaves, Olímpio Hiroshi Miyagaki

Publication date: 18 March 2015

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-014-0236-x

zbMATH Keywords

nonnegative solutioncritical exponent\((p,q)\)-Laplacian

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Critical exponents in context of PDEs (35B33) Higher-order elliptic equations (35J30) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (17)

\((p, q)\) systems with critical terms in \(\mathbb{R}^N\) ⋮ Existence result for a class of quasilinear elliptic equations with (\(p\)-\(q\))-Laplacian and vanishing potentials ⋮ Existence and asymptotic behaviour for a Kirchhoff type equation with variable critical growth exponent ⋮ Existence of solutions for critical (p,q)-Laplacian equations in ℝN ⋮ Schrödinger-Poisson system with zero mass in \(\mathbb{R}^2\) involving \((2, q)\)-Laplacian: existence, asymptotic behavior and regularity of solutions ⋮ Nontrivial weak solutions for a \((p,q)\)-Laplacian equation involving discontinuities with critical exponent ⋮ Multiplicity of solutions to class of nonlocal elliptic problems with critical exponents ⋮ Existence of solutions for supercritical \((p, 2)\)-Laplace equations ⋮ Solutions to a \((p_1, \ldots ,p_n)\)-Laplacian problem with Hardy potentials ⋮ Existence and multiplicity of solutions for a weighted \((p,q)\)-Laplacian problem on the Heisenberg Lie groups ⋮ Multiplicity results for \((p, q)\)-Laplacian equations with critical exponent in \(\mathbb{R}^N\) and negative energy ⋮ Existence of positive solutions for a class of quasilinear elliptic problems with exponential growth via the Nehari manifold method ⋮ Existence and concentration of positive solutions for a critical \(p\)\&\(q\) equation ⋮ Existence of infinitely many solutions for the \((p, q)\)-Laplace equation ⋮ Existence for \((p, q)\) critical systems in the Heisenberg group ⋮ Existence of continuous eigenvalues for a class of parametric problems involving the \((p,2)\)-Laplacian operator ⋮ On symmetric solutions for \((p, q)\)-Laplacian equations in \(\mathbb{R}^N\) with critical terms

Cites Work

• Unnamed Item
• Unnamed Item
• A class of \(p\)-\(q\)-Laplacian type equation with concave-convex nonlinearities in bounded domain
• Existence of positive solutions for a class of \(p\&q\) elliptic problems with critical growth on \(\mathbb R^N\)
• Multiplicity of positive solutions to a \(p\)--\(q\)-Laplacian equation involving critical nonlinearity
• The concentration-compactness principle in the calculus of variations. The limit case. I
• The concentration-compactness principle in the calculus of variations. The limit case. II
• Multiple solutions for the p\&q-Laplacian problem with critical exponents
• The existence of nontrivial solutions to nonlinear elliptic equation of \(p\)-\(q\)-Laplacian type on \(\mathbb R^N\)
• 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
• Multiplicity of positive solutions for some quasilinear elliptic equations in \(\mathbb{R}^N\) with critical Sobolev exponent
• A class of \(p\)-\(q\)-Laplacian type equation with potentials eigenvalue problem in \(\mathbb{R}^N\)
• The existence of a nontrivial solution to the \(p{\&}q\)-Laplacian problem with nonlinearity asymptotic to \(u^{p - 1}\) at infinity in \(\mathbb R^N\)
• Multiplicity and Concentration of Positive Solutions for a Class of Quasilinear Problems
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• Existence of positive solutions for m-Laplacian equations in N involving critical Sobolev exponents
• Stability in Obstacle Problems.
• Extrema problems with critical sobolev exponents on unbounded domains

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