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- W4385245544 abstract "We study positive solutions to the steady state reaction diffusion systems of the form: begin{equation} left{begin{array}{ll} -Delta u = lambda f(v)+mu h(u), & Omega, -Delta v = lambda g(u)+mu q(v),& Omega, frac{partial u}{partial eta}+sqrt[]{lambda +mu}, u=0,& partialOmega, frac{partial v}{partial eta}+sqrt[]{lambda +mu}, v=0, & partialOmega, end{array}right. end{equation} where ${lambda,mu>0}$ are positive parameters, ${Omega}$ is a bounded in $mathbb{R}^{N}$$(N>1)$ with smooth boundary ${partial Omega}$, or ${Omega=(0,1)}$, ${ frac{partial z}{partial eta} }$ is the outward normal derivative of $z$. Here $f, g, h, qin C^{2} [0,r)cap C[0,infty)$ for some $r>0$. Further, we assume that $f, g, h$ and $q$ are increasing functions such that $f(0) = g(0) = h(0) = {q}(0) = 0$, $f^prime(0), g^prime(0), h^prime(0), q^prime(0) > 0$, and $limlimits_{sto infty}frac{f(M g(s))}{s}=0$ for all $M>0$. Under certain additional assumptions on $f, g, h$ and $ q$ we prove our existence and multiplicity results. Our existence and multiplicity results are proved using sub-super solution methods." @default.
- W4385245544 created "2023-07-26" @default.
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- W4385245544 date "2023-07-22" @default.
- W4385245544 modified "2023-09-25" @default.
- W4385245544 title "On the existence and multiplicity of positive solutions to classes of steady state reaction diffusion systems with multiple parameters" @default.
- W4385245544 doi "https://doi.org/10.48550/arxiv.2307.12000" @default.
- W4385245544 hasPublicationYear "2023" @default.
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