1,720,977 research outputs found
Morse index and symmetry for elliptic problems with nonlinear mixed boundary conditions
Full text linkWe consider an elliptic problem of the type where Ω is a bounded Lipschitz domain in R N with a cylindrical symmetry, ν stands for the outer normal and. Under a Morse index condition, we prove cylindrical symmetry results for solutions of the above problem. As an intermediate step, we relate the Morse index of a solution of the nonlinear problem to the eigenvalues of the following linear eigenvalue problem For this one, we construct sequences of eigenvalues and provide variational characterization of them, following the usual approach for the Dirichlet case, but working in the product Hilbert space L 2 (Ω) × L 2 (Γ2)
Sectional symmetry of solutions of elliptic systems in cylindrical domains
Full text linkIn this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in [6, 9, 16, 18]
Monotonicity and symmetry of solutions of p-Laplace equations,via the moving plane method
No full textSectional symmetry of solutions of elliptic systems in cylindrical domains
No full textIn this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains.
The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in
cite{DaPaSys, DaGlPa1, Pa, PaWe}
Some nonexistence results for positive solutions of elliptic equations in unbounded domains
No full textSome nonexistence results for positive solutions of elliptic equations in unbounded domains
No full textWe prove some Liouville type theorems for positive solutions of semilinear elliptic equations in the whole space , , and in the half space with different boundary conditions, using the technique based on the Kelvin transform and the Alexandrov-Serrin method of moving hyperplanes. In particular we get new nonexistence results for elliptic problems in half spaces satisfying mixed (Dirichlet-Neumann) boundary conditions
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