Positive solutions of a one-dimensional indefinite capillarity-type problem: a variational approach

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• 作者：Juliá ; n Ló ; pez-Gó ; mez^a ; ^{julian@mat.ucm.es} ; Pierpaolo Omari^b ; ^{omari@units.it} ; Sabrina Rivetti^b ; ^{sabrina.rivetti@gmail.com}
• 关键词：primary ; 35J93 ; 34B18 ; secondary ; 34B15 ; 35B65 ; 35D10 ; 35J20 ; 49Q20 ; 53A10 ; 76D45
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2335-2392
• 全文大小：613 K
• 卷排序：262

文摘

We prove the existence and the multiplicity of positive solutions of the one-dimensional capillarity-type problem−(u′/1+(u′)2)′=a(x)f(u),u′(0)=0,u′(1)=0, where a∈L1(0,1)a∈L1(0,1) changes sign and f:[0,+∞)→[0,+∞) is continuous and has a power-like behavior at the origin and at infinity. Our approach is variational and relies on a regularization procedure that yields bounded variation solutions which are of class Wloc2,1, and hence satisfy the equation pointwise almost everywhere, on each open interval where the weight function a has a constant sign.