Positive solutions for semipositon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Φ</mml:mi> </mml:math> -Laplacian involving nonlocal term in Orlicz–Sobolev space

This paper establishes the existence of positive weak solutions for a class of semipositone Kirchhoff-type problems involving nonlocal operators and anisotropic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Φ</mml:mi> </mml:math> -Laplacians. By combining variational methods with careful asymptotic analysis, we prove that for sufficiently small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>a</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:math> , the problem admits a positive solution. Our results extend previous work on semipositone problems to the nonlocal Kirchhoff setting, overcoming challenges arising from the interplay between the nonlocal term and the indefinite nonlinearity.