Solvability of some third-order boundary value problems with asymmetric unbounded nonlinearities Original Research Article

In this paper, we present existence and location results for the third-order separated boundary value problems u‴(t)=f(t,u(t),u′(t),u″(t)),u‴(t)=f(t,u(t),u′(t),u″(t)), Turn MathJax on with the boundary conditions View the MathML sourceu(a)=A,u″(a)=B,u″(b)=C Turn MathJax on or View the MathML sourceu(a)=A,c1u′(a)-c2u″(a)=B,c3u′(b)+c4u″(b)=C, Turn MathJax on with c1,c2,c3,c4∈R+c1,c2,c3,c4∈R+ and A,B,C∈RA,B,C∈R. We assume f:[a,b]×R3→Rf:[a,b]×R3→R is a continuous function satisfying one-sided Nagumo-type condition which allows an asymmetric unbounded behaviour. The arguments used concern Leray–Schauder degree and lower and upper solution techniques.