Existence and multiplicity of symmetric solutions for a class of singular elliptic problems

Symmetric solutions for a class of singular biharmonic elliptic systems involving critical exponents

“…(1.3). Very recently, Deng and Huang [7][8][9] extended the results in [5,6] to the scalar weighted elliptic problems in a bounded G-symmetric domain. Besides, we also mention that when μ = s = 0 and the right-hand side term |x| −s u 2 * (s)−1 is replaced by u q−1 (1 < q < 2N N−2 or q = 2N N−2 ) in (1.2), some elegant results of G-symmetric solutions of (1.2) were established in [10][11][12].…”

Radial Nonlinear Elliptic Problems with Singular or Vanishing Potentials

“…When A = 1 the differential operator is the usual laplacian, and this kind of problems have been much studied in last years, with different sets of hypotheses on the nonlinearity f and the potentials V, K. Much work has been devoted in particular to problems in which such potentials can be vanishing or divergent at 0 and ∞, because this prevents the use of standard embeddings between Sobolev spaces of radial functions, and new embedding and compactness results must be proved (see for example [1], [2], [3], [4], [9], [10], [11], [12], [13], [14], [19], [20], [21], and the references therein). The case in which the potential A is not trivial has been studied in [22], [15], [18] for the p-laplacian equation, in [16] and [17] for bounded domains, and in [23] for exterior domains. The typical result obtained in these works says, roughly speaking, that given suitable asymptotic behavior at 0 and ∞ for the potentials, there is a suitable range of exponent q such that, if f behaves like the power t q−1 , then problem (1.1) has a radial solution.…”