Abstract
We study the existence of positive solutions for second‐order nonlinear differential equations with nonseparated boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a nonlinear alternative principle of Leray‐Schauder. Recent results in the literature are generalized and significantly improved.
Highlights
In this paper, we establish the positive periodic solutions for the following singular differential equation:− pxyqxyfx, y, y, 0 ≤ x ≤ T, 1.1 and boundary conditions y0 yT, y1 0 y1 T, 1.2 where p, q ∈ C R/T Z, the nonlinearity f ∈ C R/T Z × 0, ∞ × R, R, and y 1 xpxyx denotes the quasi-derivative of y x
We study the existence of positive solutions for second-order nonlinear differential equations with nonseparated boundary conditions
The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder
Summary
We establish the positive periodic solutions for the following singular differential equation:− pxyqxyfx, y, y , 0 ≤ x ≤ T, 1.1 and boundary conditions y0 yT, y1 0 y1 T , 1.2 where p, q ∈ C R/T Z , the nonlinearity f ∈ C R/T Z × 0, ∞ × R, R , and y 1 xpxyx denotes the quasi-derivative of y x. We study the existence of positive solutions for second-order nonlinear differential equations with nonseparated boundary conditions. We establish the positive periodic solutions for the following singular differential equation:
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