Weak solvability of nonlinear elliptic equations involving variable exponents
Ahmed Aberqi, Jaouad Bennouna, Omar Benslimane, Maria Alessandra Ragusa, Dipartimento di Matematica e Informatica, Universitá di Catania, Catania, Italy
Abstract
We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the $ ( p( m ), \, q( m ) )- $ equation and the nonlinearity is superlinear but does not fulfil the Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a $ ( p( m ), \, q( m ) ) $ equation that highlights the applicability of our theoretical results is also provided.
Topics & Concepts
MathematicsNonlinear systemBoundary value problemSobolev spaceVariable (mathematics)Mathematical analysisDirichlet boundary conditionCritical exponentElliptic curvePure mathematicsPhysicsGeometryQuantum mechanicsScalingNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis