Published in Advances in Nonlinear Analysis
We consider a nonlinear Robin problem driven by the (p, q)-Laplacian and a parametric reaction exhibiting the competition of a concave term and of a resonant perturbation. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on ℝ̊+ = (0, +∞). Also, we determine the continuity propertie...
Published in Advances in Nonlinear Analysis
Various strategies are available to construct iteratively a common fixed point of nonexpansive operators by activating only a block of operators at each iteration. In the more challenging class of composite fixed point problems involving operators that do not share common fixed points, current methods require the activation of all the operators at ...
Published in Advances in Nonlinear Analysis
This paper deals with existence and multiplicity of positive solutions to the following class of nonlocal equations with critical nonlinearity: (−Δ)su−γu|x|2s=K(x)|u|2s∗(t)−2u|x|t+f(x)inRN,u∈H˙s(RN), $$\begin{array}{} \displaystyle \begin{cases} (-{\it\Delta})^s u -\gamma\dfrac{u}{|x|^{2s}}=K(x)\dfrac{|u|^{2^*_s(t)-2}u}{|x|^t}+f(x) \quad\mbox{in}\q...
Published in Advances in Nonlinear Analysis
In this article, our aim is to establish a generalized version of Lions-type theorem for the p-Laplacian. As an application of this theorem, we consider the existence of ground state solution for the quasilinear elliptic equation with the critical growth.
Published in Advances in Nonlinear Analysis
In this paper, we prove the existence of multiple solutions for the following sixth-order p(x)-Kirchhoff-type problem −M∫Ω1p(x)|∇Δu|p(x)dxΔp(x)3u=λf(x)|u|q(x)−2u+g(x)|u|r(x)−2u+h(x)inΩ,u=Δu=Δ2u=0,on∂Ω, $$\begin{array}{} \displaystyle \begin{cases} -M\left( \int\limits_{\it\Omega} \frac{1}{p(x)}|\nabla {\it\Delta} u|^{p(x)}dx\right){\it\Delta}^3_{p(...
Published in Advances in Nonlinear Analysis
We show the nonlinear ergodic theorem for monotone 1-Lipschitz mappings in uniformly convex spaces: if C is a bounded closed convex subset of an ordered uniformly convex space (X, ∣·∣, ⪯), T:C → C a monotone 1-Lipschitz mapping and x ⪯ T(x), then the sequence of averages 1n∑i=0n−1Ti(x) $ \frac{1}{n}\sum\nolimits_{i=0}^{n-1}T^{i}(x) $ converges weak...
Published in Advances in Nonlinear Analysis
We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α $\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0
Published in Advances in Nonlinear Analysis
We consider the following p-harmonic problem Δ(|Δu|p−2Δu)+m|u|p−2u=f(x,u),x∈RN,u∈W2,p(RN), $$\begin{array}{} \displaystyle \left\{ \displaystyle\begin{array}{ll} \displaystyle {\it\Delta} (|{\it\Delta} u|^{p-2}{\it\Delta} u)+m|u|^{p-2}u=f(x,u), \ \ x\in {\mathbb R}^N, \\ u \in W^{2,p}({\mathbb R}^N), \end{array} \right. \end{array}$$ where m > 0 is...
Published in Advances in Nonlinear Analysis
The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. The case of the boundary value with a nonzero flow rate is considered. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In the first pa...
Published in Advances in Nonlinear Analysis
The initial boundary value problem for the non-stationary Navier-Stokes equations is studied in 2D bounded domain with a power cusp singular point O on the boundary. We consider the case where the boundary value has a nonzero flux over the boundary. In this case there is a source/sink in O and the solution necessary has infinite energy integral. In...
