Some remarks on profile decomposition theorems

DOI10.1515/ans-2015-5049zbMath1361.46025OpenAlexW2538619010MaRDI QIDQ329879

Giuseppe Devillanova, Sergio Solimini

Publication date: 24 October 2016

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2015-5049

zbMATH Keywords

multiscale analysisconcentration-compactnessprofile decompositions

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Critical exponents in context of PDEs (35B33)

Related Items

Multiplicity of solutions for a class of fractional \(p(x,\cdot)\)-Kirchhoff-type problems without the Ambrosetti-Rabinowitz condition ⋮ Existence in the nonlinear Schrödinger equation with bounded magnetic field ⋮ Existence and multiplicity results for critical anisotropic Kirchhoff-type problems with nonlocal nonlinearities ⋮ Profile decomposition in Sobolev spaces and decomposition of integral functionals. I: Inhomogeneous case ⋮ On the existence of multiple solutions for fractional Brezis–Nirenberg‐type equations ⋮ Multiscale weak compactness in metric spaces ⋮ On nonlinear Schrödinger equations on the hyperbolic space ⋮ Concentration phenomenon of solutions for a class of Kirchhoff-type equations with critical growth ⋮ Combined effects for magnetic Laplace equations with lack of compactness ⋮ Nonradial solutions of nonlinear scalar field equations ⋮ Multiple positive solutions for critical elliptic problem with singularity ⋮ Asymptotic behavior for non-autonomous fractional stochastic Ginzburg–Landau equations on unbounded domains ⋮ The Minkowski's inequalities via \(\psi\)-Riemann-Liouville fractional integral operators ⋮ On a fractional \(p-q\) Laplacian equation with critical nonlinearity ⋮ Nonlinear Schrödinger equation with bounded magnetic field ⋮ Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity

Cites Work

• A global compactness result for elliptic boundary value problems involving limiting nonlinearities
• On the defect of compactness in Banach spaces
• Analysis of the lack of compactness in the critical Sobolev embeddings
• A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev space
• Synchronic and Asynchronic Descriptions of Irrigation Problems
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• On weak convergence in metric spaces
• Equivalent Norms and the Fixed Point Property for Nonexpansive Mappings
• Remarks on Some Fixed Point Theorems
• Description of the lack of compactness for the Sobolev imbedding
• Unnamed Item
• Unnamed Item