The Ambrosetti–Prodi problem for gradient elliptic systems with critical homogeneous nonlinearity

Abstract

In this work we study the systemwhere H is a 2 * ≡ 2N/(N − 2) positively homogeneous function, G is a lower order perturbation, w + = max{w, 0} and f 1 , f 2 ∈ L r (Ω), r > N. Using the Mountain Pass Theorem we prove existence of two solutions. If N = 3, 4 and 5, an additional hypothesis over the subcritical term is needed.

Existence and multiplicity results for critical growth polyharmonic elliptic systems

“…In recent years, existence and multiplicity results for nonlinear elliptic systems with variational structure have been extensively studied ( and the references therein). Motivated by the works of , we focus on the general case m , n ≥ 1 and F positively homogeneous of degree m 霴 , we shall extend the results of to the critical polyharmonic and multiple equations case.…”

“…In recent years, existence and multiplicity results for nonlinear elliptic systems with variational structure have been extensively studied ( [10][11][12][13][14][15][16][17][18][19][20][21][22] and the references therein). Motivated by the works of [8][9][10]13], we focus on the general case m, n 1 and F positively homogeneous of degree m ?…”

Multiple solutions for p-Laplacian systems with critical homogeneous nonlinearity

“…Thus it is necessary for us to investigate the critical p-Laplacian systems (1.1) deeply. For more similar problems, we refer to [8][9][10][11][12][13][14][15][16][17], and references therein.…”

Infinitely many sign-changing solutions for a class of critical elliptic systems with Neumann conditions

“…For the system case, (1.1) with the Dirichlet boundary condition was studied, for instance, in [8,9,22,33,37,39] (see also the references therein). In [21] some of the above results for quasilinear problems involving the p-laplacian operator were extended.…”