| Summary: | We study a nonlocal Dirichlet problem with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>(</mo><mi>b</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>)</mo><mo>,</mo><mi>q</mi><mo>(</mo><mi>b</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>)</mo><mo>)</mo></mrow></semantics></math></inline-formula>-Laplacian operator and integrable data on a bounded domain with smooth boundary. We establish the existence of at least one weak solution in the case the variable exponents of the leading operator depend on the solution <i>u</i>, without assuming any growth conditions on <i>g</i>. The proof is based on the characterization of the energy functional associated to the problem, using the methods of the calculus of variations.
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