Generalized Prescribed Scalar Curvature Type Equation on a Compact Manifold of Negative Scalar Curvature

Existence and multiplicity of solutions to elliptic equations of fourth order on compact manifolds

“…More recently [2] the authors have extended the work of Rauzy to the case of the so called generalized prescribed scalar curvature type equation…”

“…with respect to the norm u 2,2 = 2 l=0 ∇ l u 2 . Let H 2 be the space H 2 2 endowed with the equivalent norm…”

“…When the manifold (M, g) is Einstein, the Paneitz Since 1990 many results have been established for precise functions a, h and f. D.E. Edmunds, D. Fortunato, E. Jannelli ( [8]) proved for n ≥ 8 that if λ ∈ (0, λ 1 ), with λ 1 is the first eigenvalue of ∆ 2 In 1995, R. Van der Vorst ( [12]) obtained the same results as D.E. Edmunds, D. Fortunato, E. Jannelli.…”

Existence and multiplicity results for nonlinear critical Neumann problem on compact Riemannian manifolds

“…For example, in case of equation (1.1) without boundary 2 Y. Maliki NoDEA condition, some existence and multiplicity results on compact and complete manifolds have been obtained by [6,[8][9][10][11]13,21]. Recently, in [18], using the variational method, the authors proved an existence result for problem (1.1) on solid torus in R 3 under the conditions that either the function f is positive and K is arbitrary or f is nonnegative and K is positive.…”

“…Note that the techniques in [27] have been adapted for equation (1.1) without boundary condition in [10] and for a Q-curvature equation in [7].…”