‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.

Exact (approximate) controllability and exact observability of stochastic singular systems in Banach spaces are discussed. Firstly, the condition for existence uniqueness mild solution to is given by GE-semigroup spaces. Secondly, necessary sufficient conditions considered derived terms GE-semigroup, dual principle given. Thirdly, an illustrative example

We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. control. Existence, uniqueness, and stability solutions are studied from point view generic theory. Within suitable topological space dynamics cost functionals, we prove that, for “nearly all” games (in Baire category sense) best reply map single-...

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.