1,720,971 research outputs found
Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level
No full text
Symmetry and nonexistence of low Morse index solutions in unbounded domains
No full textIn this paper we prove symmetry results for classical solutions of semilinear elliptic equations in the whole RN or in the exterior of a ball, N≥2, in the case when the nonlinearity is either convex or has a convex first derivative. More precisely we prove that solutions having Morse index j≤N are foliated Schwarz symmetric, i.e. they are axially symmetric with respect to an axis passing through the origin and nonincreasing in the polar angle from this axis. From this we deduce some nonexistence results for positive or sign changing solutions in the case when the nonlinearity does not depend explicitly on the space variable.
Nous démontrons des résultats de symétrie de solutions classiques de problèmes elliptiques semilinéaires dans RN ou à l'extérieur d'une boule dans les cas N≥2 où la non-linéarité est convexe et la dérivée est aussi convexe. Plus précisément, nous démontrons que toute solution dont l'indice de Morse est inférieur ou égal à N est à symétrie axiale et monotone relativement à l'angle polaire. Partant de ce résultat nous déduisons des théorèmes de non-existence de solutions positives ou de solutions qui changent de signe
Existence and nonexistence of entire solutions for non-cooperative cubic elliptic systems
No full textRadial symmetry of positive solutions in nonlinear polyharmonic Dirichlet problems
No full textWe extend the symmetry result of Gidas-Ni-Nirenberg to semilinear polyharmonic Dirichlet problems in the unit ball. In the proof we develop a new variant of the method of moving planes relying on fine estimates for the Green function of the polyharmonic operator. We also consider minimizers for subcritical higher order Sobolev embeddings. For embeddings into weighted spaces with a radially symmetric weight function, we show that the minimizers are at least axially symmetric. This result is sharp since we exhibit examples of minimizers which do not have full radial symmetr
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Critical growth biharmonic elliptic problems under Steklov-type boundary conditions
No full textWe study the fourth-order nonlinear critical problem in a smooth, bounded domain , , subject to the boundary conditions on . We provide estimates for the range of parameters for which this problem admits a positive solution. If the domain is the unit ball, we obtain an almost complete description
On a fourth order Steklov eigenvalue problem
No full textWe study a biharmonic Stekloff eigenvalue problem. We prove some new results and we collect and refine a number of known
results. Moreover, we highlight the main open problems still to be solved
Positivity, symmetry and uniqueness for minimizers of second order Sobolev inequalities
No full textWe prove that minimizers for subcritical second-order Sobolev embeddings
in the unit ball are unique, positive and radially symmetric. Since the proofs of
the corresponding first-order results cannot be extended to the present situation, we
apply new and recently developed techniques
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