Nontrivial solutions of elliptic systems with nonlinearities may not have asymptotic limits

DOI10.1016/J.JMAA.2022.126907zbMath1506.35069OpenAlexW4311173390MaRDI QIDQ2680413

Jiabao Su, Rushun Tian, Yutong Chen, Ming-Zheng Sun

Publication date: 2 January 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2022.126907

zbMATH Keywords

Dirichlet problemexistencequasilinear elliptic system

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations (35J62) Boundary value problems for second-order elliptic systems (35J57)

Cites Work

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• Solutions to a gradient system with resonance at both zero and infinity
• Solutions of elliptic problems with nonlinearities of linear growth
• Multiplicity of solutions for gradient systems with strong resonance at higher eigenvalues
• Multiple solutions for semilinear elliptic boundary value problems with double resonance
• Critical point theory and Hamiltonian systems
• Nontrivial periodic solutions for the asymptotically linear Hamiltonian systems with resonance at infinity
• A variational approach to subquadratic perturbations of elliptic systems
• On the Morse indices of sign changing solutions of nonlinear elliptic problems
• Infinite dimensional Morse theory and multiple solution problems
• An extension of the Hess-Kato theorem to elliptic systems and its applications to multiple solution problems
• A unified approach to a class of strongly indefinite functionals
• Minimax theorems
• Homology of saddle point reduction and applications to resonant elliptic systems
• Multiplicity of solutions for gradient systems using Landesman-Lazer conditions
• Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero
• Gradient systems with sublinear term near the origin and asymptotically linear term near infinity
• Multiplicity of solutions for resonant elliptic systems
• An elliptic resonance problem with multiple solutions
• Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Solutions of asymptotically linear operator equations via morse theory
• Semilinear elliptic resonant problems at higher eigenvalue with unbounded nonlinear terms
• Variational elliptic problems which are nonquadratic at infinity
• Multiple solutions for indefinite functionals and applications to asymptotically linear problems
• A variational approach to noncooperative elliptic systems
• MULTIPLE SOLUTIONS FOR RESONANT ELLIPTIC SYSTEMS VIA REDUCTION METHOD
• Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
• Multiplicity results for semilinear elliptic equations with resonance at higher eigenvalues
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems
• Solution of nonlinear equations having asymptotic limits at zero and infinity.
• Principal eigenvalue for weight matrix in elliptic systems
• Semilinear elliptic boundary value problems with double resonance between two consecutive eigenvalues

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