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We discuss the existence of solutions for a class of nonlinear equations driven by the fractional p‐Laplacian operator of the form (−Δ)psu+λsV(x,λ)|u|p−2u=f(x,u)inRN, where 0ps and λ is a positive parameter.… Click to show full abstract
We discuss the existence of solutions for a class of nonlinear equations driven by the fractional p‐Laplacian operator of the form (−Δ)psu+λsV(x,λ)|u|p−2u=f(x,u)inRN, where 0ps and λ is a positive parameter. By combining variational techniques with a version of the mountain pass theorem without Palais‐Small (PS) condition, we establish the existence of nontrivial solutions for the above equation under certain appropriate assumptions on nonlinearity and weight functions.
Keywords:
class;
equations potential;
potential depending;
class fractional;
fractional laplacian;
laplacian equations
Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019
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Journal Title: Mathematical Methods in the Applied Sciences
Year Published: 2019
Link to full text (if available)
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recommendations!