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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Abstract

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

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

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369083479

Mathematical Reviews number (MathSciNet)
MR1296134

Zentralblatt MATH identifier
0818.34013

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

Citation

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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