论文标题
一些新的加权紧凑型嵌入结果以及特征值罗宾问题的弱解决方案的存在
Some new weighted compact embeddings results and existence of weak solutions for eigenvalue Robin problem
论文作者
论文摘要
通过应用Mountain Pass引理，Ekeland和Ricceri的变化原理，源定理，我们证明了以下robin问题的存在和多样化，以下解决方案\ begin \ begin {equation*} \ left \ left \ leet {\ begin {array} aray} {array} u \ right \ vert ^{ ^{p（x）-2} \ frac {\ partial u} {\ partial \ upsilon}+β（x）\ left \ welet \ vert u \ right \ right \ vert ^{p（x）-2} -2} u = 0， \ end {equation*}在空间中的某些适当条件下$ w_ {a，b}^{1，p（。
By applying Mountain Pass Lemma, Ekeland's and Ricceri's variational principle, Fountain Theorem, we prove the existence and multiplicity of solutions for the following Robin problem \begin{equation*} \left\{ \begin{array}{cc} -\text{div}\left( a(x)\left\vert \nabla u\right\vert ^{p(x)-2}\nabla u\right) =λb(x)\left\vert u\right\vert ^{q(x)-2}u, & x\in Ω\\ a(x)\left\vert \nabla u\right\vert ^{p(x)-2}\frac{\partial u}{\partial \upsilon }+β(x)\left\vert u\right\vert ^{p(x)-2}u=0, & x\in \partial Ω, \end{array} \right. \end{equation*} under some appropriate conditions in the space $W_{a,b}^{1,p(.)}\left( Ω\right).$
