Solvability of a generalized third-order left focal problem at resonance in Banach spaces

Title:

Solvability of a generalized third-order left focal problem at resonance in Banach spaces

Creator:

Zhang, Youwei

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:79cfac72-7448-4959-9474-98e46bc6f363
uuid:79cfac72-7448-4959-9474-98e46bc6f363
doi:10.21136/MB.2013.143510

Subject:

Fredholm operator, coincidence degree, left focal problem, nontrivial solution, and resonance

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

This paper deals with the generalized nonlinear third-order left focal problem at resonance (p(t)u ′′(t))′ − q(t)u(t) = f(t, u(t), u′ (t), u′′(t)), t ∈ ]t0, T[, m(u(t0), u′′(t0)) = 0, n(u(T), u′ (T)) = 0, l(u(ξ), u′ (ξ), u′′(ξ)) = 0, where the nonlinear term is a Carathéodory function and contains explicitly the first and second-order derivatives of the unknown function. The boundary conditions that we study are quite general, involve a linearity and include, as particular cases, Sturm-Liouville boundary conditions. Under certain growth conditions on the nonlinearity, we establish the existence of the nontrivial solutions by using the topological degree technique as well as some recent generalizations of this technique. Our results are generalizations and extensions of the results of several authors. An application is included to illustrate the results obtained.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

361-382

Source:

Mathematica bohemica | 2013 Volume:138 | Number:4

Harvested from:

CDK

Metadata only:

false