Advances in Differential Equations

Solvability conditions for semilinear elliptic boundary value problems at resonance with bounded and unbounded nonlinear terms

Stephen B. Robinson and Th. Runst

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Abstract

In this paper we generalize and improve some well-known solvability conditions for semilinear elliptic boundary value problems at resonance within the context of Besov and Triebel-Lizorkin spaces. In particular we will show that many such solvability conditions can be viewed as special cases of a single generalized Landesman-Lazer condition. Our methods apply an adaptation of Leray-Schauder degree ideas to quasi-Banach spaces.

Article information

Source
Adv. Differential Equations, Volume 3, Number 4 (1998), 595-624.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366292565

Mathematical Reviews number (MathSciNet)
MR1659238

Zentralblatt MATH identifier
0948.35056

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 46N20: Applications to differential and integral equations 47H15 47N20: Applications to differential and integral equations

Citation

Robinson, Stephen B.; Runst, Th. Solvability conditions for semilinear elliptic boundary value problems at resonance with bounded and unbounded nonlinear terms. Adv. Differential Equations 3 (1998), no. 4, 595--624. https://projecteuclid.org/euclid.ade/1366292565


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