Two-point boundary value problems for 4th order ordinary differential equations

Mariam Manjikashvili; Sulkhan Mukhigulashvili;


The new optimal efficient sufficient conditions are established for solvability and uniqueness of a solution of the linear and nonlinear fourth order ordinary differential equations $$ u^{(4)}(t)= p(t)u(t)+ q(t) \quad \text{for} \quad t\in [a,\,b], $$ $$ u^{(4)}(t)= p(t)u(t)+ f(t,u(t)) \quad \text{for} \quad t\in [a,\,b], $$ under the following two-point boundary conditions $$ u^{(i)}(a)=0,\quad u^{(i)}(b)=0 \;\; (i=0,1), $$ and $$ u^{(i)}(a)=0 \;\; (i=0,1,2),\quad u(b)=0, $$ where $p\in L([a,\,b];\,R)$ is a nonconstant sign function and $f\in K([a,\,b]\times R; R).$

Vol. 25 (2024), No. 1, pp. 399-409

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