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Keywords:
iteration; symmetric and monotone positive solution; nonlinear boundary value problem; $p$-Laplacian
iteration; symmetric and monotone positive solution; nonlinear boundary value problem; $p$-Laplacian
Summary:
In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation $(\phi _p(u^{\prime }))^{\prime }+q(t)f(u)=0$, $0<t<1$, where $\phi _p(s):=|s|^{p-2}s$, $p>1$, subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient $q(t)$ may be singular at $t=0,1$.
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