<p style='text-indent:20px;'>We examine the following degenerate elliptic system:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ -\Delta_{s} u \! = v^p, \quad v\! u^\theta, \;\; u, v>0 \;\;\mbox{in }\; \mathbb{R}^N \mathbb{R}^{N_1}\times \mathbb{R}^{N_2}, \quad\mbox{where}\;\; s \geq 0\;\; \mbox{and} \;\;p...

In this paper we prove Liouville type theorem for the stationary Navier–Stokes equations in \(\mathbb {R}^3\) under assumptions on relative decays of velocity, pressure and head pressure. More precisely, show that any smooth solution (u, p) satisfying \(u(x) \rightarrow 0\) as \(|x|\rightarrow +\infty \) condition finite Dirichlet integral \(\int _{\mathbb {R}^3} | \nabla u|^2 dx <+\infty is tr...

We prove a Filippov-Gronwall type inequality for solutions of a nonconvex secondorder differential inclusion of Sturm-Liouville type.

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

in this paper, the homotopy perturbation method (hpm) is applied to obtain an approximate solution of the fractional bratu-type equations. the convergence of the method is also studied. the fractional derivatives are described in the modied riemann-liouville sense. the results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional...

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.