107 research outputs found
On Uniqueness of Boundary Blow-up Solutions of a Class of Nonlinear Elliptic Equations
We study boundary blow-up solutions of semilinear elliptic equations
with , or with , where is a second order
elliptic operator with measurable coefficients. Several uniqueness theorems and
an existence theorem are obtained.Comment: To appear in Comm. Partial Differential Equations; 10 page
Equivalence classes of the second order ODEs with the constant Cartan invariant
Second order ordinary differential equations that possesses the constant
invariant are investigated. Four basic types of these equations were found. For
every type the complete list of nonequivalent equations is issued. As the
exampes the equivalence problem for the Painleve II equation, Painleve III
equation with three zero parameters, Emden equations and for some other
equations is solved
Asymptotically radial solutions to an elliptic problem on expanding annular domains in Riemannian manifolds with radial symmetry
Non-existence and uniqueness results for supercritical semilinear elliptic equations
Non-existence and uniqueness results are proved for several local and
non-local supercritical bifurcation problems involving a semilinear elliptic
equation depending on a parameter. The domain is star-shaped but no other
symmetry assumption is required. Uniqueness holds when the bifurcation
parameter is in a certain range. Our approach can be seen, in some cases, as an
extension of non-existence results for non-trivial solutions. It is based on
Rellich-Pohozaev type estimates. Semilinear elliptic equations naturally arise
in many applications, for instance in astrophysics, hydrodynamics or
thermodynamics. We simplify the proof of earlier results by K. Schmitt and R.
Schaaf in the so-called local multiplicative case, extend them to the case of a
non-local dependence on the bifurcation parameter and to the additive case,
both in local and non-local settings.Comment: Annales Henri Poincar\'e (2009) to appea
Studies on the cell location of cyclic 3\u27, 5\u27- -guanosine monophosphate-dependent protein kinase in cerebellum.
‘Large’ solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
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