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LARGE SOLUTIONS OF QUASILINEAR ELLIPTIC EQUATION OF MIXED TYPE
Yuan Zhang,Zuodong Yang 한국전산응용수학회 2014 Journal of applied mathematics & informatics Vol.32 No.5
We consider the equation △mu = p(x)uα+q(x)uβ on RN(N ≥ 2), where p; q are nonnegative continuous functions and 0 < α ≤ . Under several hypotheses on p(χ) and q(χ), we obtain existence and nonexistence of blow-up solutions both for the superlinear and sublinear cases. Existence and nonexistence of entire bounded solutions are established as well.
EXISTENCE OF SOLUTIONS FOR BOUNDARY BLOW-UP QUASILINEAR ELLIPTIC SYSTEMS
Qing Miao,Zuodong Yang 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, we are concerned with the quasilinear elliptic systems with boundary blow-up conditions in a smooth bounded domain. Using the method of lower and upper solutions,we prove the sufficient conditions for the existence of the positive solution. Our main results are new and extend the results in [Mingxin Wang, Lei Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Analysis(In Press)].
EXISTENCE OF LARGE SOLUTIONS FOR A QUASILINEAR ELLIPTIC PROBLEM
Yan Sun,Zuodong Yang 한국전산응용수학회 2010 Journal of applied mathematics & informatics Vol.28 No.1
We consider a class of elliptic problems of a logistic type −div(|∇u|m−2∇u) = w(x)υq − (a(x))m/2f(u)in a bounded domain of Rⁿ with boundary δΩ of class C², υlδΩ = +∞,w ∈ L∞(Ω0, 0 < q < 1 and a ∈ Cα(Ω), R+ is non-negative for some α ∈ (0, 1), where R+ = [0,∞). Under suitable growth assumptions on a, b and f, we show the exact blow-up rate and uniqueness of the large solutions. Our proof is based on the method of sub-supersolution.
BLOW UP OF SOLUTIONS TO A SEMILINEAR PARABOLIC SYSTEM WITH NONLOCAL SOURCE AND NONLOCAL BOUNDARY
Peng, Congming,Yang, Zuodong The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper we investigate the blow up properties of the positive solutions to a semi linear parabolic system with coupled nonlocal sources $u_t={\Delta}u+k_1{\int}_{\Omega}u^{\alpha}(y,t)v^p(y,t)dy,\;v_t={\Delta}_v+k_2{\int}_{\Omega}u^q(y,t)v^{\beta}(y,t)dy$ with non local Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set.
Blow up of solutions to a semilinear parabolic system with nonlocal source and nonlocal boundary
Congming Peng,Zuodong Yang 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.5
In this paper we investigate the blow up properties of the positive solutions to a semilinear parabolic system with coupled nonlocal sources ut = Δu+k1 ∫Ωuα(y, t)vp(y, t)dy, vt = Δv+k2∫Ω uq (y, t)vβ(y, t)dy with nonlocal Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set.. In this paper we investigate the blow up properties of the positive solutions to a semilinear parabolic system with coupled nonlocal sources ut = Δu+k1 ∫Ωuα(y, t)vp(y, t)dy, vt = Δv+k2∫Ω uq (y, t)vβ(y, t)dy with nonlocal Dirichlet boundary conditions. We establish the conditions for global and non-global solutions respectively and obtain its blow up set..
Yin, Honghui,Yang, Zuodong The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.3
In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.
BOUNDARY BEHAVIOR OF LARGE SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS
Juan Sun,Zuodong Yang 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3
In this paper, our main purpose is to consider the quasilinear elliptic equation div(|∇_u|^(p-2)∇u) = (p-1)f(u)on a bounded smooth domain Ω ⊂ R^N, where P > 1. N > 1 and f is a smooth, increasing function in [0, ∞]. We get some estimates of a soultion u satisfying u(x) → ∞ as d(x, ∂Ω) → 0 under different conditions on f.
ON GROUND STATE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC EQUATIONS
Yin, Honghui,Yang, Zuodong The Korean Society for Computational and Applied M 2011 Journal of applied mathematics & informatics Vol.29 No.3
In this paper, our main purpose is to establish the existence of positive bounded entire solutions of second order quasilinear elliptic equation on $R^N$. we obtained the results under different suitable conditions on the locally H$\"{o}$lder continuous nonlinearity f(x, u), we needn't any mono-tonicity condition about the nonlinearity.
EXISTENCE OF SOLUTIONS FOR BOUNDARY BLOW-UP QUASILINEAR ELLIPTIC SYSTEMS
Miao, Qing,Yang, Zuodong The Korean Society for Computational and Applied M 2010 Journal of applied mathematics & informatics Vol.28 No.3
In this paper, we are concerned with the quasilinear elliptic systems with boundary blow-up conditions in a smooth bounded domain. Using the method of lower and upper solutions, we prove the sufficient conditions for the existence of the positive solution. Our main results are new and extend the results in [Mingxin Wang, Lei Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Analysis(In Press)].
EXISTENCE OF RADIAL POSITIVE SOLUTIONS FOR A QUSILINEAR NON-POSITONE PROBLEM IN A BALL
WANG, WEIHUI,YANG, ZUODONG The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.5
In this paper, we prove existence of radial positive solutions for the following boundary value problem