Liouville theorem for elliptic equations with nonlinear boundary value conditions and finite Morse indices

DOI10.1016/j.jmaa.2014.07.010zbMath1297.35065OpenAlexW2051824900MaRDI QIDQ401371

Xiaohui Yu

Publication date: 26 August 2014

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.2014.07.010

zbMATH Keywords

Liouville theoremMorse indexno nontrivial bounded solutionsnonlinear boundary value condition

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Semilinear elliptic equations (35J61) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (13)

Liouville theorem for elliptic equations with mixed boundary value conditions and finite Morse indices ⋮ Stable solutions of \(-\Delta u+\lambda u=|u|^{p-1}u\) in strips ⋮ Liouville theorem for some elliptic equations with weights and finite Morse indices ⋮ Liouville theorem for Choquard equation with finite Morse indices ⋮ Liouville-type theorems for elliptic equations in half-space with mixed boundary value conditions ⋮ Liouville theorems for the weighted Lane-Emden equation with finite Morse indices ⋮ Classification of finite Morse index solutions for Robin boundary value problems ⋮ Liouville theorems for Hénon type elliptic equation with mixed boundary conditions and finite Morse index ⋮ Some Liouville theorems for Hénon type equations in half-space with nonlinear boundary value conditions and finite Morse indices ⋮ Liouville results for \(m\)-Laplace equations in half-space and strips with mixed boundary value conditions and finite Morse index ⋮ Positive solutions with single and multi-peak for semilinear elliptic equations with nonlinear boundary condition in the half-space ⋮ Nonexistence results on the space or the half space of \(-\Delta u+\lambda u = \vert u\vert ^{p-1}u \) via the Morse index ⋮ Liouville type theorem for a singular elliptic equation with finite Morse index

Cites Work

• Liouville type theorem for nonlinear elliptic equation with general nonlinearity
• A priori estimates for superlinear and subcritical elliptic equations: The Neumann boundary condition case
• Nonnegative solutions for nonlinear elliptic systems
• Liouville-type theorems and harnack-type inequalities for semilinear elliptic equations
• Superlinear indefinite elliptic problems and Pohozyaev type identities
• On a semilinear elliptic problem without (PS) condition.
• Uniqueness theorems through the method of moving spheres
• Solutions of superlinear elliptic equations and their Morse indices. I, II
• Nontrivial solutions of Schrödinger equations with indefinite nonlinearities
• Solutions of the mixed boundary problem and their Morse indices
• A priori bounds for positive solutions of nonlinear elliptic equations
• Solutions of superlinear elliptic equations and their morse indices
• Spike-layered solutions for an elliptic system with Neumann boundary conditions

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