## Differential and Integral Equations

### The existence of solutions to a class of semilinear differential equations

#### 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

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