In 2007, Tian and Ge [15] generalized the existence results to the p-Laplacian system (1).
In [12, 13], Lian et al. generalized their existence results to unbounded solutions, and somewhat weakened the conditions in [14].
Motivated by the above work, our paper aims to discuss the existence and uniqueness of solutions for BSDEs driven by time-changed Lévy noises when the generator g satisfies monotonicity, continuity and general growth conditions with respect to y, which generalize the existence and uniqueness result of [1].
Presented theorems extend and generalize some existence results in the literature.
Our result of the ergodic theorem of Baillon's type improves and generalizes many existence theorems of this type of problem.
Our approach, then, is based on (and generalizes) the existence theorem of [Simon, L., Zame, W., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58 (4), 861 872] designed for discontinuous games.
Moreover, our result generalizes the existence result obtained in [12] as the equation considered in [12] is a special case of our system (1.1) with (p(t)=q(t)=s=1).
Theorem 4.1 and Theorem 4.2 improve and generalize many existence results in the literature; see for example Theorem 9 in [10], Theorem 4.1 in [11], Theorem 2 in [12] and Theorem 1 in [13].
Using a gradient flow approach initiated by S. Brendle, we generalize the existence theorem for the prescribing Q-curvature equation on S2 (Gauss curvature) by M. Struwe (2005) [14] and on S4 by Malchiodi and Struwe (2006) [12] to Sn for all even n with the similar assumption on the prescribed curvature candidate f.
In Section 3, in a suitably chosen framework, we verify that the conditions in the abstract critical point theorems in [16] are satisfied, then we generalize the existence of multiplicity solutions for fractional Laplacian problems to the one for fractional p-Laplacian problems.
