New competition phenomena in Dirichlet problems

Existence of entire solutions for a class of quasilinear elliptic equations

“…Similarly, by Hölder's inequality and (1.3), we obtain 18) and 19) with C 3 = C 3 (K). Combining (3.17)-(3.19), and recalling that (λ n ) n is bounded, we get the claim.…”

“…In [2] also solvability and multiplicity were proved under various assumptions on the weights and on the parameter λ ∈ R. The famous results of [3] were partially extended by De Figueiredo et al to indefinite nonlinearities for the semilinear case in [10] and for the p-Laplacian operator in [11]. For recent contributions on related semilinear Dirichlet problems in bounded domains we refer to [8,18] and on equations in the entire R N to [19], and to the references therein. The equation considered here is in the spirit of the previous papers, even if most of them deal with problems not directly comparable to ours.…”

Multiplicity results to a class of variational-hemivariational inequalities

“…Likewise, we draw attention to a paper of Kristály-Moroşanu in which a new competition phenomena between oscillatory and pure power terms has been described (cf. [26]). It should be noted that our variational-hemivariational inequality is equivalent to the multi-valued variational inequality…”

Variational analysis for a nonlinear elliptic problem on the Sierpiński gasket

“…Only a few papers deal with non-linearities having no symmetry properties; see, for instance, the papers of Omari and Zanolin [24,25] and the recent work of Kristály and Moroşanu [17] for perturbed Dirichlet equations.…”