Solitons in Several Space Dimensions:¶Derrick's Problem and¶Infinitely Many Solutions

By Vieri Benci, Pietro d'Avenia, D. Fortunato, Lorenzo Pisani. 2000

298 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a7627ba9a2091a88fb1c3c8df623689e31f33c5d

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Overdetermined problems with possibly degenerate ellipticity, a geometric approach (2006, background): “We also refer to [ 3 , 4] for more general applications to quantum physics.”
(N,q)‐Laplacian problems with critical Trudinger‐Moser nonlinearities (2014, background): “appears in a wide range of applications that include biophysics [12], plasma physics [25], reaction-diffusion equations [1, 6], and models of elementary particles [10, 4, 2].”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “R˘adulescu–Repovš[2]ontransonicﬂows,Benci–D’Avenia– Fortunato–Pisani[11]onquantumphysicsandCherﬁls-Il yasov [13] on reaction diffusion systems.”
Critical groups computations on a class of Sobolev banach spaces via morse index (2003, unknown): “…involving p -laplacian Hence we shall focus on a class of Banach spaces which are the natural variational (cid:6) (cid:6) (cid:6) (g) | g (cid:7) (t) | (cid:2) c 1 | t | q + c 2 with c 1 , c 2 positive 1 ,p ( of the quasilinear elliptic problem p propagation phenomena of solitary waves (cf. [2,3]).”
Large and Small Solutions of a Class of Quasilinear Elliptic Eigenvalue Problems (2002, background): “) Other applications of such problems are found when seeking soliton-like solutions of Lorentz invariant equations; see [1, 2].”
Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance (2014, background): “We mention that equations like (1) (we call them (p,2)-equations for short) are important in quantum physics in the search for solitons, see Benci, D’Avenia, Fortunato, & Pisani [7].”
Wang’s multiplicity result for superlinear (,)–equations without the Ambrosetti–Rabinowitz condition (2013, background): “Moreover, the (p, 2)-equation is important in quantum physics for the existence of solitons; see Benci–D’Avenia–Fortunato–Pisani [2].”