论文标题
在涉及$ p（x）$ - laplacian的准线性方程中非线性低阶项的影响
Effect of Non-linear Lower Order Terms in Quasilinear Equations Involving the $p(x)$-Laplacian
论文作者
论文摘要
在这项工作中，我们研究了$ w_0^{1，p（\ cdot）} $的存在 - 涉及$ p（\ cdot）$ - laplacian操作员的以下边界价值问题的解决方案： \ begin {equation*} \左\ lbrace \ begin {array} {l} -Δ_{p（x）} u+| \ nabla u |^{q（x）} =λg（x） \ quad \ textnormal {in}ω \ qquad \，\，\，\，\，\ quad \ quad \ qquad \ quad \ quad u = 0，\，\，\，\ quad \ text \ text {on} \partialΩ。 \ end {array} \正确的。 \ end {等式*}在变量指数上适当的范围内。就增长指数$ q $和$η$而言，我们对上述问题具有非负解决方案的所有$λ> 0 $的解决方案。
In this work, we study the existence of $W_0^{1, p(\cdot)}$-solutions to the following boundary value problem involving the $p(\cdot)$-Laplacian operator: \begin{equation*} \left\lbrace \begin{array}{l} -Δ_{p(x)}u+|\nabla u|^{q(x)}=λg(x)u^{η(x)}+f(x), \quad\textnormal{ in } Ω, \\\qquad \,\,\,\,\,\quad \quad\qquad\quad u\geq 0, \quad\textnormal{ in } Ω \qquad \,\,\,\,\,\quad \quad\qquad\quad u= 0, \,\,\quad \text{on } \partialΩ. \end{array} \right. \end{equation*}under appropriate ranges on the variable exponents. We give assumptions on $f$ and $g$ in terms of the growth exponents $q$ and $η$ under which the above problem has a non-negative solution for all $λ> 0$.
