Qualitative properties and classification of nonnegative solutions to \(-\Delta u=f(u)\) in unbounded domains when \(f(0) < 0\)
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Publication:515353
DOI10.4171/RMI/918zbMath1377.35042arXiv1405.3428OpenAlexW2962811895MaRDI QIDQ515353
Berardino Sciunzi, Alberto Farina
Publication date: 13 March 2017
Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1405.3428
Boundary value problems for second-order elliptic equations (35J25) Semilinear elliptic equations (35J61) Symmetries, invariants, etc. in context of PDEs (35B06) Comparison principles in context of PDEs (35B51)
Related Items (13)
Some results about semilinear elliptic problems on half-spaces ⋮ Classification and Liouville-type theorems for semilinear elliptic equations in unbounded domains ⋮ Nonnegative solutions of semilinear elliptic equations in half-spaces ⋮ Monotonicity of positive solutions to quasilinear elliptic equations in half-spaces with a changing-sign nonlinearity ⋮ On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results ⋮ Qualitative properties of nonnegative solutions of some semilinear elliptic equations in cylindrical domains ⋮ A note on the monotonicity of solutions for fractional equations in half-spaces ⋮ Monotonicity of Positive Solutions to − Δp u + a(u)|∇u|q = f(u) in the Half-Plane in the Case $$p\leqslant 2$$ ⋮ Monotonicity and symmetry of nonnegative solutions to \(-\Delta u=f(u)\) in half-planes and strips ⋮ Monotonicity of solutions for some nonlocal elliptic problems in half-spaces ⋮ Symmetry results in the half-space for a semi-linear fractional Laplace equation ⋮ Second order estimate on transition layers ⋮ Some symmetry results and Liouville-type theorems for solutions to semilinear equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Symmetry and uniqueness of nonnegative solutions of some problems in the halfspace
- Monotonicity of solutions of fully nonlinear uniformly elliptic equations in the half-plane
- Monotonicity of the solutions of some quasilinear elliptic equations in the half-plane, and applications.
- Some remarks on half space problems
- On the classification of solutions of the Lane-Emden equation on unbounded domains of \(\mathbb R^N\)
- Inequalities for second-order elliptic equations with applications to unbounded domains. I
- Monotonicity and nonexistence results to cooperative systems in the half space
- Bernstein and De Giorgi type problems: new results via a geometric approach
- Existence and non-existence results for semilinear elliptic problems in unbounded domains
- On the method of moving planes and the sliding method
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