A Nonlinear Dirichlet Problem on the Unit Ball

By W. Rother. 2009

225 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/09dc6406bcc6704395c7f8263411f0a3831f5dc9

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In Applied Mathematics

Citations in the corpus

Liouville-type theorems and bounds of solutions of Hardy-Hénon equations (2012, methodology): “Ni [19] proved the existence of a radial solution in a larger range, namely for 1 < p < pS (a), by using the Mountain Pass Lemma in a space of radial functions.”
Radial and non radial solutions for Hardy–Hénon type elliptic systems (2010, background): “On the other hand, if is a ball, then one has the existence of a radial solution in a larger range, namely for 2 < p+1 < 2(N+α) N−2 (see [23]), and the non-existence of nontrivial solutions in the range: p+1 ≥ 2(N+α) N−2 by a Pohozaev-type identity for radial functions.”
The critical hyperbola for a Hamiltonian elliptic system with weights (2008, methodology): “For scalar Hénon equations and properties we refer to [6,30,33,34] and the references therein.”
Sobolev type embedding and quasilinear elliptic equations with radial potentials (2011, background): “The case α = 0, p = 2 (known as Ni’s inequality) was due to [23] where this inequality was given in the unit ball of RN .”
Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space (2013, background): “Problems of this type have been widely studied (see for instance [23,24,27,29] and the references therein).”
Weighted Sobolev embedding with unbounded and decaying radial potentials (2007, background): “Lemma 1 extends a result in [21] which was for p = 2 and known as Ni’s inequality.”
Infinitely many nonradial solutions for the Hénon equation with critical growth (2013, background): “Ni [9] first proved the existence of a radial solution for any α > 0.”
Nonlinear schrodinger equations with unbounded and decaying radial potentials (2007, unknown): “For a problem in a bounded domain this was observed in [18].”
Sobolev inequalities with symmetry (2009, background): “For s = 1 with n ≥ 3, the inequality (1) reduces to Ni’s inequality [6, 7].”
Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space (2013, background): “and we point out that, as shown in [18], the above problem has a positive radial solution provided that 1 < q < N+2m+2 N−2 and N 3, m > 0.”