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EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS

Chunmei Miao|Wei-Gao Ge|Zhaojun Zhang
ํ•œ๊ตญ์ˆ˜ํ•™๊ต์œกํ•™ํšŒ|2014.08|์ด๋ก ์ˆ˜ํ•™๊ณผ ๊ต์ง์ˆ˜ํ•™ (Theoretical Mathematics and Pedagogical Mathematics)|์ œ21๊ถŒ ์ œ3ํ˜ธ|pp. 147-163

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positive solutionssingular impulsive diยฎerential equationsintegral boundary conditionsLeray-Schauder degree
์ฃผ์ œ๋ถ„๋ฅ˜์ˆ˜ํ•™

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In this paper, we study the existence of positive solutions for singularimpulsive differential equations with integral boundary conditions๐‘ข"(๐‘ก)+๐‘ž(๐‘ก)๐‘“(๐‘ก,๐‘ข(๐‘ก),๐‘ข'(๐‘ก))=0,๐‘กโˆŠ๐•',โˆ†๐‘ข(๐‘ก๐‘˜)=๐ผ๐‘˜(๐‘ข(๐‘ก๐‘˜),๐‘ข'(๐‘ก๐‘˜)),๐‘˜=1,2,โ€ฆ,๐‘,โˆ†๐‘ข'(๐‘ก๐‘˜)=-๐ฟ๐‘˜(๐‘ข(๐‘ก๐‘˜),๐‘ข'(๐‘ก๐‘˜)),๐‘˜=1,2,โ€ฆ,๐‘,๐‘ข(0)=โˆซ10๐˜จ(๐‘ก)๐‘ข(๐‘ก)๐‘‘๐‘ก, ๐‘ข'(1)=0,where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based onthe theory of Leray-Schauder degree, together with a truncation technique. Somerecent results in the literature are generalized and improved.

Abstract

In this paper, we study the existence of positive solutions for singularimpulsive differential equations with integral boundary conditions๐‘ข"(๐‘ก)+๐‘ž(๐‘ก)๐‘“(๐‘ก,๐‘ข(๐‘ก),๐‘ข'(๐‘ก))=0,๐‘กโˆŠ๐•',โˆ†๐‘ข(๐‘ก๐‘˜)=๐ผ๐‘˜(๐‘ข(๐‘ก๐‘˜),๐‘ข'(๐‘ก๐‘˜)),๐‘˜=1,2,โ€ฆ,๐‘,โˆ†๐‘ข'(๐‘ก๐‘˜)=-๐ฟ๐‘˜(๐‘ข(๐‘ก๐‘˜),๐‘ข'(๐‘ก๐‘˜)),๐‘˜=1,2,โ€ฆ,๐‘,๐‘ข(0)=โˆซ10๐˜จ(๐‘ก)๐‘ข(๐‘ก)๐‘‘๐‘ก, ๐‘ข'(1)=0,where the nonlinearity f(t, u, v) may be singular at v = 0. The proof is based onthe theory of Leray-Schauder degree, together with a truncation technique. Somerecent results in the literature are generalized and improved.

์ฐธ๊ณ ๋ฌธํ—Œ (26)

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