Elliptic equations involving nonlocal operator with exponent variable
Existence and multiplicity of solutions for Elliptic equations involving nonlocal operator with exponent variable
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In this work, we are interested in the existence and multiplicity of nontrivial solutions for a class of elliptic problems. The first problem deals with the existence of nontrivial weak solutions to a class of elliptic equations involving a general nonlocal integrodifferential operator with variable exponent, two real parameters, and two weight functions, which can be sign-changing in a smooth bounded domain. The second problem deals with the existence and multiplicity of weak solutions involving the same operator, variable exponents without Ambrosetti and Rabinowitz type growth conditions and...
In this work, we are interested in the existence and multiplicity of nontrivial solutions for a class of elliptic problems. The first problem deals with the existence of nontrivial weak solutions to a class of elliptic equations involving a general nonlocal integrodifferential operator with variable exponent, two real parameters, and two weight functions, which can be sign-changing in a smooth bounded domain. The second problem deals with the existence and multiplicity of weak solutions involving the same operator, variable exponents without Ambrosetti and Rabinowitz type growth conditions and a positive real parameter in a smooth bounded domain.
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