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1
Content available remote

Existence results for a class of quasilinear integrodifferential equations of Volterra-Hammerstein type with nonlinear boundary conditions

100%
Yang Z.
Annales Polonici Mathematici
|
2004
|
tom 84
|
nr 3
211-218
EN
The existence of a solution for a class of quasilinear integrodifferential equations of Volterra-Hammerstein type with nonlinear boundary conditions is established. Such equations occur in the study of the p-Laplace equation, generalized reaction-diffusion theory, non-Newtonian fluid theory, and in the study of turbulent flows of a gas in a porous medium. The results are obtained by using upper and lower solutions, and extend some previously known results.
2
Content available remote

Multiplicity results for a class of concave-convex elliptic systems involving sign-changing weight functions

64%
Yin H., Yang Z.
Annales Polonici Mathematici
|
2011
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tom 102
|
nr 1
51-71
EN
Our main purpose is to establish the existence of weak solutions of second order quasilinear elliptic systems ⎧ $-Δ_pu + |u|^{p-2}u = f_{1λ₁}(x) |u|^{q-2}u + 2α/(α+β) g_μ|u|^{α-2} u|v|^β$, x ∈ Ω, ⎨ $-Δ_pv + |v|^{p-2}v = f_{2λ₂}(x) |v|^{q-2}v + 2β/(α+β) g_μ|u|^α|v|^{β-2}v$, x ∈ Ω, ⎩ u = v = 0, x∈ ∂Ω, where 1 < q < p < N and $Ω ⊂ ℝ^N$ is an open bounded smooth domain. Here λ₁, λ₂, μ ≥ 0 and $f_{iλ_i}(x) = λ_if_{i+}(x) + f_{i-}(x)$ (i = 1,2) are sign-changing functions, where $f_{i±}(x) = max{±f_i(x),0}$, $g_μ(x) = a(x) + μb(x)$, and $Δ_p u = div(|∇u|^{p-2}∇u)$ denotes the p-Laplace operator. We use variational methods.
3
Content available remote

Solutions to a class of singular quasilinear elliptic equations

64%
Wei L., Yang Z.
Annales Polonici Mathematici
|
2010
|
tom 98
|
nr 3
231-240
EN
We study the existence of positive solutions to ⎧ $div(|∇u|^{p-2}∇u) + q(x)u^{-γ} = 0$ on Ω, ⎨ ⎩ u = 0 on ∂Ω, where Ω is $ℝ^{N}$ or an unbounded domain, q(x) is locally Hölder continuous on Ω and p > 1, γ > -(p-1).
4
Content available remote

Existence and asymptotic behavior of positive solutions for elliptic systems with nonstandard growth conditions

64%
Yin H., Yang Z.
Annales Polonici Mathematici
|
2012
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tom 104
|
nr 3
293-308
EN
Our main purpose is to establish the existence of a positive solution of the system ⎧$-∆_{p(x)}u = F(x,u,v)$, x ∈ Ω, ⎨$-∆_{q(x)}v = H(x,u,v)$, x ∈ Ω, ⎩u = v = 0, x ∈ ∂Ω, where $Ω ⊂ ℝ^{N}$ is a bounded domain with C² boundary, $F(x,u,v) = λ^{p(x)}[g(x)a(u) + f(v)]$, $H(x,u,v) = λ^{q(x})[g(x)b(v) + h(u)]$, λ > 0 is a parameter, p(x),q(x) are functions which satisfy some conditions, and $-∆_{p(x)}u = -div(|∇u|^{p(x)-2}∇u)$ is called the p(x)-Laplacian. We give existence results and consider the asymptotic behavior of solutions near the boundary. We do not assume any symmetry conditions on the system.
5
Content available remote

Asymptotics for quasilinear elliptic non-positone problems

64%
Yang Z., Lu Q.
Annales Polonici Mathematici
|
2002
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tom 79
|
nr 1
85-95
EN
In the recent years, many results have been established on positive solutions for boundary value problems of the form $-div(|∇u(x)|^{p-2} ∇u(x)) = λf(u(x))$ in Ω, u(x)=0 on ∂Ω, where λ > 0, Ω is a bounded smooth domain and f(s) ≥ 0 for s ≥ 0. In this paper, a priori estimates of positive radial solutions are presented when N > p > 1, Ω is an N-ball or an annulus and f ∈ C¹(0,∞) ∪ C⁰([0,∞)) with f(0) < 0 (non-positone).
6
Content available remote

Existence and nonexistence of solutions for a quasilinear elliptic system

64%
Li Q., Yang Z.
Annales Polonici Mathematici
|
2015
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tom 113
|
nr 2
155-164
EN
By a sub-super solution argument, we study the existence of positive solutions for the system ⎧$-Δ_{p}u = a₁(x)F₁(x,u,v)$ in Ω, ⎪$-Δ_{q}v = a₂(x)F₂(x,u,v)$ in Ω, ⎨u,v > 0 in Ω, ⎩u = v = 0 on ∂Ω, where Ω is a bounded domain in $ℝ^{N}$ with smooth boundary or $Ω = ℝ^{N}$. A nonexistence result is obtained for radially symmetric solutions.
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