论文标题
与具有功能术语的奇异非线性方程相关的边界价值问题
Boundary value problems associated with singular strongly nonlinear equations with functional terms
论文作者
论文摘要
我们研究与奇异，非线性差分方程相关的边界价值问题，其功能性$$ \ big（φ（k（t）\，x'（t））\ big）\ f（t，t，\ nathcal {g} _x（t））这些方程式非常普遍，因为存在严格增加的同构$φ$，即所谓的$φ$ -laplacian操作员，其非负函数$ k $，该函数可能会在一组无效的措施中消失，此外，功能性术语$ \ nterm $ \ nathcal $ \ nathcal {g} _x _x _x _x _x $。我们从适当的弱意义上寻找解决方案，属于Sobolev空间$ W^{1,1}（[a，b]）$。在存在良好的上和下溶液以及合适的nagumo型生长条件的假设下，我们证明存在通过固定点参数所致。
We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big(Φ(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,ρ(t, x'(t)) = 0$$ on a compact interval $[a,b]$. These equations are quite general due to the presence of a strictly increasing homeomorphism $Φ$, the so-called $Φ$-Laplacian operator, of a nonnegative function $k$, which may vanish on a set of null measure, and moreover of a functional term $\mathcal{G}_x$. We look for solutions, in a suitable weak sense, which belong to the Sobolev space $W^{1,1}([a,b])$. Under the assumptions of the existence of a well-ordered pair of upper and lower solutions and of a suitable Nagumo-type growth condition, we prove an existence result by means of fixed point arguments.
