Differential and Integral Equations

The existence of solutions to a class of semilinear differential equations

Yin Xi Huang and Gerhard Metzen

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We will study the existence of solutions of $$ -(\alpha^{p-1}(t)|u'|^{p-2}u')'= f(t,u)+h(t) \quad \text{in $[0,1]$}, $$ subject to various boundary conditions and $p>1$. In addition, we will give a detailed characterization of the eigenvalues and the Fucik spectrum of the corresponding differential operators. We use the Sturm comparison theorem and degree theory.

Article information

Differential Integral Equations, Volume 8, Number 2 (1995), 429-452.

First available in Project Euclid: 20 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34B15: Nonlinear boundary value problems
Secondary: 47H15 47N20: Applications to differential and integral equations


Huang, Yin Xi; Metzen, Gerhard. The existence of solutions to a class of semilinear differential equations. Differential Integral Equations 8 (1995), no. 2, 429--452. https://projecteuclid.org/euclid.die/1369083479

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