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We prove that the four-point boundary value problem $$\begin{aligned} -\left[ \phi (u') \right] ^{\prime }=f(t,u, u'), \quad u(0)=\alpha u(\xi ), \quad u(T)=\beta u(\eta ), \end{aligned}$$-ϕ(u′)′=f(t,u,u′),u(0)=αu(ξ),u(T)=βu(η),where $$f:[0,T] \times \mathbb {R}^2 \rightarrow… Click to show full abstract
We prove that the four-point boundary value problem $$\begin{aligned} -\left[ \phi (u') \right] ^{\prime }=f(t,u, u'), \quad u(0)=\alpha u(\xi ), \quad u(T)=\beta u(\eta ), \end{aligned}$$-ϕ(u′)′=f(t,u,u′),u(0)=αu(ξ),u(T)=βu(η),where $$f:[0,T] \times \mathbb {R}^2 \rightarrow \mathbb {R}$$f:[0,T]×R2→R is continuous, $$\alpha , \; \beta \in [0,1)$$α,β∈[0,1), $$0<\xi< \eta
Keywords:
value problem;
phi;
boundary value;
point;
point boundary;
four point
Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2019
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Journal Title: Journal of Fixed Point Theory and Applications
Year Published: 2019
Link to full text (if available)
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recommendations!