Nonlinear elliptic equations at resonance where the nonlinearity depends essentially on the derivative

DOI10.1016/0022-0396(80)90005-4zbMath0413.35032OpenAlexW1978585084MaRDI QIDQ1260533

Karen Singkofer, R. Kent Nagle, Ken Pothoven

Publication date: 1980

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90005-4

zbMATH Keywords

existence of solutionsdegree theorymonotone operatorsunbounded linear operatorLandesman-Lazer conditionsalternative methodbounded, coercive bilinear formnonlinear elliptic boundary-value problems

Mathematics Subject Classification ID

Monotone operators and generalizations (47H05) Nonlinear elliptic equations (35J60) Degree, winding number (55M25) Other special methods applied to PDEs (35A25)

Related Items (3)

Resonant semilinear problems with nonlinear term depending on the derivative ⋮ Nonselfadjoint semilinear elliptic boundary value problems ⋮ A Fourier analysis approach to elliptic equations with critical potentials and nonlinear derivative terms

Cites Work

• Existence and multiplicity of solutions to nonlinear differential equations at resonance
• Existence theorems for nonlinear boundary value problems at resonance
• Ranges of nonlinear asymptotically linear operators
• Alternative problems and monotonicity
• A nonlinear elliptic boundary value problem at resonance
• Existence and multiplicity results for nonlinear elliptic problems with linear part at resonance. The case of the simple eigenvalue
• Strongly nonlinear perturbations of nonnegative boundary value problems with kernel
• A sharp sufficient condition for solution of a nonlinear elliptic boundary value problem
• Equations with unbounded nonlinearities
• An Abstract Existence Theorem at Resonance
• On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems
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