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- W3011214504 abstract "This paper is concerned with the existence and uniqueness of positive solution for the fourth order Kirchhoff type problem $$left{begin{array}{ll} u''''(x)-(a+bint_0^1(u'(x))^2dx)u''(x)=lambda f(u(x)), xin(0,1), u(0)=u(1)=u''(0)=u''(1)=0, end{array} right. $$ where $a>0, bgeq 0$ are constants, $lambdain mathbb{R}$ is a parameter. For the case $f(u)equiv u$, we use an argument based on the linear eigenvalue problems of fourth order equations and their properties to show that there exists a unique positive solution for all $lambda>lambda_{1,a}$, here $lambda_{1,a}$ is the first eigenvalue of the above problem with $b=0$; For the case $f$ is sublinear, we prove that there exists a unique positive solution for all $lambda>0$ and no positive solution for $lambda<0$ by using bifurcation method." @default.
- W3011214504 created "2020-03-23" @default.
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- W3011214504 date "2020-03-10" @default.
- W3011214504 modified "2023-09-24" @default.
- W3011214504 title "Existence and uniqueness of positive solutions for Kirchhoff type beam equations" @default.
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- W3011214504 doi "https://doi.org/10.48550/arxiv.2003.04746" @default.
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