This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

in this paper we prove existence the common fixed point with different conditions for $alpha-psi$-contractive mappings. and generalize weakly zamfirescu map in to modified weakly zamfirescu map.

We exhibit new examples of double Kodaira fibrations by using finite Galois covers a product $\Sigma_b \times \Sigma_b$, where $\Sigma_b$ is smooth projective curve genus $b \geq 2$. Each cover obtained providing an explicit group epimorphism from the pure braid $\mathsf{P}_2(\Sigma_b)$ to some Heisenberg group. In this way, we are able show that every $b$ base fibration; moreover, number pairw...

Probably the most basic invariant of a finitely generated group is its rank, ie the minimal number of elements needed to generate it. In general the rank of a group is not computable. For instance, there are examples, due to Baumslag, Miller and Short [3], of hyperbolics groups showing that there is no uniform algorithm solving the rank problem. Everything changes in the setting of 3–manifold g...

Eight-dimensional non-geometric heterotic strings with gauge algebra $\mathfrak{e}_8\mathfrak{e}_7$ were constructed by Malmendier and Morrison as duals of F-theory on K3 surfaces $\Lambda^{1,1}\oplus E_8\oplus E_7$ lattice polarization. Clingher, Shaska extended these constructions to eight-dimensional $\mathfrak{e}_7\mathfrak{e}_7$ E_7\oplus polarized surfaces. In this study, we analyze the p...